Associate Professor Lee Zhao

Associate Professor

Ph. D., Rutgers University, May 2003
B. A., Rutgers University, May 1998

Science

School of Mathematics & Statistics

My primary research interests are in analytic number theory. More specifically, I am interested in the analytic theory of of L-functions, exponential sums, the large sieve, elliptic curves. I joined the School of Mathematics and Statistics at �鶹��madou in 2015. For more information, please go to my .

Phone

02 9385 7086

E-mail

l.zhao@unsw.edu.au

Location

School of Mathematics and Statistics �鶹��madou AUSTRALIA SYDNEY NSW 2052 The Red Centre Room 4106

Journal articles | 2024

Gao P; Zhao L, 2024, 'Bounds for moments of quadratic Dirichlet character sums', Bulletin of the Australian Mathematical Society

Journal articles | 2024

Gao P; Zhao L, 2024, 'First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters', Journal of Number Theory, 261, pp. 125 - 142

Journal articles | 2024

Gao P; Zhao L, 2024, 'First moment of central values of some primitive Dirichlet L-functions with fixed order characters', Journal of Number Theory, 261, pp. 125 - 142,

Journal articles | 2024

Gao P; Zhao L, 2024, 'Lower Bounds for Moments of Quadratic Twists of Modular L-functions', Functiones et Approximatio Commentarii Mathematici, 71, pp. 183 - 200,

Journal articles | 2024

Gao P; Zhao L, 2024, 'Moments and one level density of sextic Hecke L-functions', Functiones et Approximatio Commentarii Mathematici, 70, pp. 7 - 28,

Journal articles | 2024

Gao P; Zhao L, 2024, 'Moments of Dirichlet $L$-functions to a fixed modulus over function fields', International Journal of Number Theory

Journal articles | 2024

Gao P; Zhao L, 2024, 'Moments of Dirichlet L-functions to a fixed modulus over function fields', International Journal of Number Theory, 20, pp. 1493 - 1513,

Journal articles | 2024

Gao P; Zhao L, 2024, 'Ratios conjecture for quadratic twists of modular $L$-functions', Research in Number Theory, 10,

Journal articles | 2024

Gao P; Zhao L, 2024, 'Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions', Acta Arithmetica

Journal articles | 2024

Gao P; Zhao L, 2024, 'Twisted first moment of quadratic and quadratic twist $L$-functions', Functiones et Approximatio Commentarii Mathematici, 70, pp. 101 - 127,

Journal articles | 2023

Corrigan C; Zhao L, 2023, 'Zero-Density Theorems for Families of Dirichlet L-functions', Bulletin of the Australian Mathematical Society, 108, pp. 224 - 235,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli', Colloquium Mathematicum, 171, pp. 61 - 77,

Journal articles | 2023

Gao P; Zhao L, 2023, 'First moment of central values of quadratic Hecke $L$-functions in the Gaussian field', International Journal of Number Theory,

Journal articles | 2023

Gao P; Zhao L, 2023, 'First moment of central values of quadratic Hecke L-functions in the Gaussian field', International Journal of Number Theory, 19, pp. 1621 - 1637,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Lower bounds for negative moments of $ζ'(ρ)$', Mathematika: a journal of pure and applied mathematics, 69, pp. 1081 - 1103,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Mean squares of quadratic twists of the Möbius function', Journal of Number Theory, 247, pp. 1 - 14,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Mean squares of quadratic twists of the Möbius function', Journal of Number Theory, 247, pp. 1 - 14,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Moments of quadratic Dirichlet L-functions over function fields', Finite Fields and Their Applications, 85, pp. 102113 - 102113,

Journal articles | 2023

Gao P; Zhao L, 2023, 'One-level density of quadratic twists of L-functions', Acta Arithmetica, 207, pp. 201 - 215,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field', Monatshefte fuer Mathematik,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Ratios conjecture for quadratic Hecke L-functions in the Gaussian field', Monatshefte fur Mathematik, 203, pp. 63 - 90,

Journal articles | 2023

Gao P; Zhao L, 2023, 'Subconvexity of a double Dirichlet series over the Gaussian field', Quarterly Journal of Mathematics, 74, pp. 1237 - 1252,

Journal articles | 2023

Gao PENG; Zhao L, 2023, 'Lower-order terms of the one-level density of a family of quadratic Hecke L-functions', Journal of the Australian Mathematical Society, 114, pp. 178 - 221,

Journal articles | 2022

Gao P; Zhao L, 2022, 'Average values of quadratic Hecke character sums', Journal of the Ramanujan Mathematical Society, 37, pp. 99 - 107,

Journal articles | 2022

Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet $L$-functions', Indagationes Mathematicae, 33, pp. 1263 - 1296,

Journal articles | 2022

Gao P; Zhao L, 2022, 'Bounds for moments of cubic and quartic Dirichlet L-functions', Indagationes Mathematicae,

Journal articles | 2022

Gao P; Zhao L, 2022, 'First Moments of Some Hecke $L$-functions of Prime Moduli', Functiones et Approximatio Commentarii Mathematici, 66, pp. 161 - 178,

Journal articles | 2022

Gao P; Zhao L, 2022, 'One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields', Journal of the Australian Mathematical Society, 112, pp. 170 - 192,

Journal articles | 2022

Gao P; Zhao L, 2022, 'The Large Sieve with Power Moduli in Imaginary Quadratic Number Fields', International Journal of Number Theory, 18, pp. 1713 - 1733,

Journal articles | 2022

Gao P; Zhao L, 2022, 'Moments of quadratic Dirichlet $L$-functions over Function Fields', Finite Fields and Their Applications

Journal articles | 2021

Gao P; Zhao L, 2021, 'Moments and One level density of certain unitary families of Hecke {$L$}-functions', Journal de Theorie des Nombres de Bordeaux, 33, pp. 1 - 16,

Journal articles | 2021

Gao P; Zhao L, 2021, 'Moments and One level density of certain unitary families of Hecke L-functions', JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 33, pp. 1 - 16,

Journal articles | 2021

Gao P; Zhao L, 2021, 'Moments of central values of quartic Dirichlet L-functions', Journal of Number Theory, 228, pp. 342 - 358,

Journal articles | 2021

Gao P; Zhao L, 2021, 'One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli', The Hardy-Ramanujan Journal, 43, pp. 173 - 187

Journal articles | 2021

Gao P; Zhao L, 2021, 'Value-distribution of quartic Hecke $L$-functions', Moscow Journal of Combinatorics and Number Theory, 10, pp. 167 - 181,

Journal articles | 2020

Gao P; Zhao L, 2020, 'First Moments of Some Hecke $L$-functions of Prime Moduli', Funct. Approx. Comment. Math., Vol. 66, 2022, No. 2, pp. 161--178,

Journal articles | 2020

Gao P; Zhao L, 2020, 'Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture', ,

Journal articles | 2020

Gao P; Zhao L, 2020, 'Mean values of cubic and quartic Dirichlet Characters', Functiones et Approximatio Commentarii Mathematici, 63, pp. 227 - 245,

Journal articles | 2020

Gao P; Zhao L, 2020, 'Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields', Journal of Number Theory, 209, pp. 359 - 377,

Journal articles | 2020

Gao P; Zhao L, 2020, 'Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$', Research in Number Theory, 6, pp. 14,

Journal articles | 2020

Gao P; Zhao L, 2020, 'One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli', Hardy-Ramanujan Journal, 43, pp. 173 - 187,

Journal articles | 2020

Gao P; Zhao L, 2020, 'One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions', Canadian Journal of Mathematics, 72, pp. 427 - 454,

Journal articles | 2019

Baier S; Lynch S; Zhao L, 2019, 'A Lower Bound for the Large Sieve with Square Moduli', Bulletin of the Australian Mathematical Society, 100, pp. 225 - 225,

Journal articles | 2019

Gao P; Zhao L, 2019, 'Average values of quadratic Hecke character sums', Journal- Ramanujan Mathematical Society, 37, pp. 99 - 107

Journal articles | 2019

Gao P; Zhao L, 2019, 'First Moment of Hecke $L$-functions with quartic characters at the central point', Mathematische Zeitschrift, 294, pp. 1841 - 1854,

Journal articles | 2019

Gao P; Zhao L, 2019, 'Lower order terms of the one level density of a family of quadratic Hecke $L$-functions', Journal of the Australian Mathematical Society

Journal articles | 2019

Gao P; Zhao L, 2019, 'Mean values of some Hecke characters', Acta Arithmetica, 187, pp. 125 - 141,

Journal articles | 2019

Gao P; Zhao L, 2019, 'PRIMES p ≡ 1 mod d AND a^(p1)/d ≡ 1 mod p', Integers, 19

Journal articles | 2019

Gao P; Zhao L, 2019, 'Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}', Integers : Electronic Journal of Combinatorial Number Theory, 19

Journal articles | 2019

Gao P; Zhao L, 2019, 'WEIGHTED FIRST MOMENTS OF SOME SPECIAL QUADRATIC DIRICHLET L-FUNCTIONS', New Zealand Journal of Mathematics, 49, pp. 31 - 40,

Journal articles | 2019

Gao P; Zhao L, 2019, 'Weighted first moments of some special quadratic Dirichlet $L$-functions', New Zealand Journal of Mathematics, 49, pp. 31 - 40

Journal articles | 2018

Gao P; Zhao L, 2018, 'Mean values of divisors of forms $n^2+Nm^2$', ,

Journal articles | 2018

Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212

Journal articles | 2017

Gao P; Zhao L, 2017, 'Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$', ,

Journal articles | 2016

Baker RC; Zhao L, 2016, 'Gaps between primes in Beatty sequences', Acta Arithmetica, 172, pp. 207 - 242,

Journal articles | 2016

Baker RC; Zhao L, 2016, 'Gaps of Smallest Possible Order between Primes in an Arithmetic Progression', International Mathematics Research Notices, 2016, pp. 7341 - 7368,

Journal articles | 2013

Baier S; Zhao L, 2013, 'On Hecke eigenvalues at primes of the form [g(n)]', Acta Arithmetica, 158, pp. 341 - 357,

Journal articles | 2013

Foo T; Zhao L, 2013, 'On primes represented by cubic polynomials', Mathematische Zeitschrift, 274, pp. 323 - 340,

Journal articles | 2012

Baier S; Browning TD; Marasingha G; Zhao L, 2012, 'Averages of shifted convolutions of d3(n)', Proceedings of the Edinburgh Mathematical Society, 55, pp. 551 - 576,

Journal articles | 2012

Gao P; Zhao L, 2012, 'Large sieve inequalities for quartic characters', Quarterly Journal of Mathematics, 63, pp. 891 - 917,

Journal articles | 2011

Foo T; Zhao L, 2011, 'On Primes Represented by Cubic Polynomials', Math. Z., 2, pp. 1 - 2

Journal articles | 2011

Gao P; Zhao L, 2011, 'One level density of low-lying zeros of families of L-functions', Compositio Mathematica, 147, pp. 1 - 18,

Journal articles | 2010

Baier S; Zhao L, 2010, 'On Hecke eigenvalues at Piatetski-Shapiro primes', Journal of the London Mathematical Society, 81, pp. 175 - 201,

Journal articles | 2009

Baier S; Zhao L, 2009, 'On primes in quadratic progressions', International Journal of Number Theory, 5, pp. 1017 - 1035,

Journal articles | 2009

Baier S; Zhao L, 2009, 'THE SATO-TATE CONJECTURE ON AVERAGE FOR SMALL ANGLES', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 361, pp. 1811 - 1832

Journal articles | 2009

Baier S; Zhao L, 2009, 'The sato-tate conjecture on average for small angles', Transactions of the American Mathematical Society, 361, pp. 1811 - 1832,

Journal articles | 2008

Baier S; Zhao L, 2008, 'An improvement for the large sieve for square moduli', Journal of Number Theory, 128, pp. 154 - 174,

Journal articles | 2008

Baier S; Zhao L, 2008, 'On the low-lying zeros of Hasse-Weil L-functions for elliptic curves', Advances in Mathematics, 219, pp. 952 - 985,

Journal articles | 2007

Baier S; Zhao L, 2007, 'Primes in quadratic progressions on average', Mathematische Annalen, 338, pp. 963 - 982,

Journal articles | 2007

Zhao L, 2007, 'Large sieve inequality with quadratic amplitudes', Monatshefte fur Mathematik, 151, pp. 165 - 173,

Journal articles | 2006

Baier S; Zhao L, 2006, 'Bombieri-Vinogradov type theorems for sparse sets of moduli', Acta Arithmetica, 125, pp. 187 - 201,

Journal articles | 2006

Zhao L, 2006, 'Oscillations of Hecke eigenvalues at shifted primes', Revista Matematica Iberoamericana, 22, pp. 323 - 337,

Journal articles | 2005

Baier S; Zhao L, 2005, 'LARGE SIEVE INEQUALITY WITH CHARACTERS FOR POWERFUL MODULI', INTERNATIONAL JOURNAL OF NUMBER THEORY, 1, pp. 265 - 279,

Journal articles | 2005

Baier S; Zhao L, 2005, 'Large Sieve Inequalities for Characters to Powerful Moduli', Int. J. Number Theory, 1, pp. 265 - 279

Journal articles | 2005

Zhao L, 2005, 'An improvement of a large sieve inequality in high dimensions', Mathematika, 52, pp. 93 - 100,

Journal articles | 2004

Zhao L, 2004, 'Large Sieve Inequalities for Special Characters to Prime Square Moduli', Functiones et Approximatio, Commentarii Mathematici, 32, pp. 99 - 106

Journal articles | 2004

Zhao L, 2004, 'Large sieve inequality with characters to square moduli', Acta Arithmetica, 112, pp. 297 - 308,
Working Papers | 2022

Gao P; Zhao L, 2022, Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$, Adam Mickiewicz University Press, ,

Working Papers | 2022

Gao P; Zhao L, 2022, Moments and one level density of sextic Hecke L-functions of Q(ω), ,

Working Papers | 2022

Gao P; Zhao L, 2022, Ratios conjecture for quadratic Hecke L-functions in the Gaussian field, ,
Preprints | 2024

Gao P; Zhao L, 2024, Bounds for Moments of Twisted Fourier coefficients of Modular Forms,

Preprints | 2024

Gao P; Zhao L, 2024, Bounds for moments of quadratic Dirichlet character sums,

Preprints | 2024

Gao P; Zhao L, 2024, Lower bounds for shifted moments of Dirichlet $L$-functions of fixed modulus,

Preprints | 2024

Gao P; Zhao L, 2024, Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli,

Preprints | 2024

Gao P; Zhao L, 2024, Ratios conjecture of quartic $L$-functions of prime moduli,

Preprints | 2024

Gao P; Zhao L, 2024, Shifted moments of quadratic Dirichlet $L$-functions,

Preprints | 2024

Gao P; Zhao L, 2024, Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions, ,

Preprints | 2024

Gao P; Zhao L, 2024, Upper bounds for shifted moments of quadratic Dirichlet $L$-functions over function fields,

Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of Hecke $L$-functions with Fixed Order Characters,

Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of quadratic Dirichlet $L$-functions,

Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters, ,

Preprints | 2023

Gao P; Zhao L, 2023, First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters,

Preprints | 2023

Gao P; Zhao L, 2023, Negative first moment of quadratic twists of $L$-functions,

Preprints | 2023

Gao P; Zhao L, 2023, Ratios conjecture for primitive quadratic Hecke $L$-functions,

Preprints | 2023

Gao P; Zhao L, 2023, Ratios conjecture for quadratic twist of modular $L$-functions, ,

Preprints | 2023

Gao P; Zhao L, 2023, Ratios conjecture of cubic $L$-functions of prime moduli,

Preprints | 2023

Gao P; Zhao L, 2023, Twisted first moment of quadratic and quadratic twist $L$-functions,

Preprints | 2023

2023, Twisted first moment of quadratic and quadratic twist $L$-functions, ,

Preprints | 2022

Corrigan CC; Zhao L, 2022, Zero-Density Theorems for Families of Dirichlet $L$-functions,

Preprints | 2022

Gao P; Zhao L, 2022, First moment of central values of quadratic Hecke $L$-functions in the Gaussian field,

Preprints | 2022

Gao P; Zhao L, 2022, Lower bounds for negative moments of $\zeta'(\rho)$,

Preprints | 2022

Gao P; Zhao L, 2022, Mean squares of quadratic twists of the Möbius function,

Preprints | 2022

Gao P; Zhao L, 2022, Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$,

Preprints | 2022

Gao P; Zhao L, 2022, Moments of Dirichlet $L$-functions to a fixed modulus over function fields, ,

Preprints | 2022

Gao P; Zhao L, 2022, Moments of quadratic Dirichlet $L$-functions over Function Fields

Preprints | 2022

Gao P; Zhao L, 2022, Non-vanishing of quadratic twists of modular $L$-functions of prime-related moduli,

Preprints | 2022

Gao P; Zhao L, 2022, One-level density of quadratic twists of $L$-functions,

Preprints | 2022

Gao P; Zhao L, 2022, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field,

Preprints | 2022

Gao P; Zhao L, 2022, Subconvexity of a double Dirichlet series over the Gaussian field,

Preprints | 2022

2022, Lower bounds for negative moments of $ζ'(ρ)$, ,

Preprints | 2022

2022, Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field, ,

Preprints | 2022

2022, Subconvexity of a double Dirichlet series over the Gaussian field, ,

Preprints | 2021

Gao P; Zhao L, 2021, Bounds for moments of cubic and quartic Dirichlet $L$-functions,

Preprints | 2021

Gao P; Zhao L, 2021, Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli,

Preprints | 2021

Gao P; Zhao L, 2021, Lower bounds for moments of quadratic twists of modular $L$-functions,

Preprints | 2021

Gao P; Zhao L, 2021, Moments of central values of quartic Dirichlet $L$-functions,

Preprints | 2019

Gao P; Zhao L, 2019, Lower order terms of the one level density of a family of quadratic Hecke $L$-functions,

Preprints | 2019

Gao P; Zhao L, 2019, Mean values of cubic and quartic Dirichlet Characters,

Preprints | 2018

Baier S; Lynch SB; Zhao L, 2018, A Lower Bound for the Large Sieve with Square Moduli,

Preprints | 2018

Gao P; Zhao L, 2018, Moments and One level density of certain unitary families of Hecke {$L$}-functions,

Preprints | 2018

Gao P; Zhao L, 2018, Value-distribution of quartic Hecke $L$-functions,

Preprints | 2017

Gao P; Zhao L, 2017, First Moment of Hecke $L$-functions with quartic characters at the central point,

Preprints | 2017

Gao P; Zhao L, 2017, Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields,

Preprints | 2017

Gao P; Zhao L, 2017, One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields,

Preprints | 2016

Shparlinski IE; Zhao L, 2016, Elliptic curves in isogeny classes,

Preprints | 2011

Foo T; Zhao L, 2011, On Primes Represented by Cubic Polynomials

Other | 2010

Baier S; Zhao L, 2010, A Subconvexity Bound for Automorphic $L$-functions for $SL(3,Z)$,

Preprints | 2009

Gao P; Zhao L, 2009, One level density of low-lying zeros of families of $L$-functions,

Preprints | 2008

Baier S; Zhao L, 2008, On Hecke Eigenvalues at Piatetski-Shapiro Primes,

Preprints | 2007

Baier S; Zhao L, 2007, On Primes Represented by Quadratic Polynomials,

Preprints | 2007

Baier S; Zhao L, 2007, On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves,

Preprints | 2006

Baier S; Zhao L, 2006, Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli,

Conference Papers | 2006

Zhao L; Baier S, 2006, 'On Primes Represented by Quadratic Polynomials', in de Koninck J; Granville A; Luca F (eds.), Anatomy of Integers, Montreal, pp. 159 - 166, presented at Anatomy of Integers, Montreal, 13 November 2006 - 17 March 2006

Preprints | 2005

Baier S; Zhao L, 2005, Large Sieve Inequalities for Characters to Powerful Moduli

Theses / Dissertations | 2003

Zhao L, 2003, Large Sieve and Exponential Sums

Faculty Research Grant, �鶹��madou Sydney Australia, 2017, 2018, 2019, 2020, 2021, 2023, 2024

Faculty Goldstar Grant, �鶹��madou Sydney Australia, 2019

Faculty Silverstar Grant, �鶹��madou Sydney Australia, 2022, 2018

Academic Research Fund Tier 1 Grant, Nanyang Tech. Univ., Singapore, Feb. 2010 – Feb. 2013

Max-Planck-Institut f¨ur Mathematik Research Grant, Bonn Germany Jan. – Jun. 2010

Academic Research Fund Tier 1 Grant, Nanyang Tech. Univ., Singapore, Jan. 2008 – Jan. 2010

Commander’s Award for Civilian Service, U. S. Mil. Acad., 2004

Davies Fellowship, US Mil. Acad. & US Army Research Lab. 2004

Analytic number theory

President, Number Theory Down Under, Sep. 2023 -- Present

My Teaching

I teach a variety of undergraduate and graduate courses in pure mathematics.

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