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Associate Professor Alina Ostafe

Associate Professor Alina Ostafe

Associate Professor
Science
School of Mathematics & Statistics
Phone
93857058
E-mail
alina.ostafe@unsw.edu.au
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 5104
  • Books | 2014
    Niederreiter H; Ostafe A; Panario D; Winterhof A, 2014, Algebraic Curves and Finite Fields Introduction, Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), Radon Series on Computational and Applied Mathematics, WALTER DE GRUYTER GMBH,
  • Book Chapters | 2017
    Ostafe A; Shparlinski IE, 2017, 'Orbits of algebraic dynamical systems in subgroups and subfields', in Elsholtz C; Grabner P (ed.), Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer, pp. 347 - 368,
    Book Chapters | 2016
    Ostafe A; Sha M, 2016, 'Counting dynamical systems over finite fields', in Contemporary Mathematics, pp. 187 - 203,
    Book Chapters | 2013
    Ostafe A; Winterhof A, 2013, 'Some applications of character sums.', in Mullen GL; Panario D (ed.), Handbook of Finite Fields, CRC Press, pp. 170 - 184,
    Book Chapters | 2013
    Ostafe A, 2013, 'Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects', in Finite Fields and Their Applications, DE GRUYTER, pp. 197 - 232,
  • Edited Books | 2014
    Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), 2014, Algebraic Curves and Finite Fields, WALTER DE GRUYTER GMBH,
  • Journal articles | 2025
    Bérczes A; Bugeaud Y; Gyory K; Mello J; Ostafe A; Sha M, 2025, 'Explicit bounds for the solutions of superelliptic equations over number fields', Forum Mathematicum, 37, pp. 135 - 158,
    Journal articles | 2024
    Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, 'Statistics of ranks, determinants and characteristic polynomials of rational matrices', Forum Mathematicum,
    Journal articles | 2024
    Bulinski K; Ostafe A; Shparlinski I, 2024, 'Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups', ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pp. 12,
    Journal articles | 2024
    Bérczes A; Bugeaud Y; Győry K; Mello J; Ostafe A; Sha M, 2024, 'Multiplicative dependence of rational values modulo approximate finitely generated groups', Mathematical Proceedings of the Cambridge Philosophical Society, 177, pp. 149 - 165,
    Journal articles | 2024
    Dietmann R; Ostafe A; Shparlinski IE, 2024, 'Discriminants of fields generated by polynomials of given height', Israel Journal of Mathematics, 260, pp. 73 - 103,
    Journal articles | 2024
    Ferraguti A; Ostafe A; Zannier U, 2024, 'Cyclotomic and abelian points in backward orbits of rational functions', Advances in Mathematics, 438, pp. 109463,
    Journal articles | 2024
    Mohammadi A; Ostafe A; Shparlinski IE, 2024, 'On some matrix counting problems', Journal of the London Mathematical Society, 110,
    Journal articles | 2024
    Ostafe A; Shparlinski IE; Voloch JF, 2024, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, 176, pp. 39 - 53,
    Journal articles | 2023
    Ostafe A; Shparlinski IE; Voloch JF, 2023, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', International Mathematics Research Notices, 2023, pp. 14196 - 14238,
    Journal articles | 2023
    Ostafe A, 2023, 'Corrigendum to: On a problem of Lang for matrix polynomials (Bulletin of the London Mathematical Society, (2022), 54, 5, (1552-1567), 10.1112/blms.12642)', Bulletin of the London Mathematical Society, 55, pp. 2086,
    Journal articles | 2022
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2022, 'On sparsity of representations of polynomials as linear combinations of exponential functions', Journal of the London Mathematical Society, 105, pp. 2076 - 2103,
    Journal articles | 2022
    Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics
    Journal articles | 2022
    Ostafe A; Shparlinski IE, 2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, 74, pp. 773 - 792,
    Journal articles | 2022
    Ostafe A, 2022, 'On a problem of Lang for matrix polynomials', Bulletin of the London Mathematical Society, 54, pp. 1552 - 1567,
    Journal articles | 2021
    Barroero F; Capuano L; Merai L; Ostafe A; Sha M, 2021, 'Multiplicative and Linear Dependence in Finite Fields and on Elliptic Curves Modulo Primes', International Mathematics Research Notices, 2022, pp. 16094 - 16137,
    Journal articles | 2021
    Bérczes A; Bugeaud Y; Győry K; Mello J; Ostafe A; Sha M, 2021, 'Multiplicative dependence of rational values modulo approximate finitely generated groups', Math. Proc. Camb. Phil. Soc., 177, pp. 149 - 165
    Journal articles | 2021
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, 104, pp. 381 - 390,
    Journal articles | 2021
    Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, 298, pp. 1187 - 1199,
    Journal articles | 2021
    Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, 27, pp. 903 - 917,
    Journal articles | 2021
    Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', ,
    Journal articles | 2021
    Ostafe A, 2021, 'On a Problem of Lang for Matrix Polynomials', ,
    Journal articles | 2020
    Barroero F; Capuano L; Mérai L; Ostafe A; Sha M, 2020, 'Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes', ,
    Journal articles | 2019
    Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2019, 'Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups', International Mathematics Research Notices,
    Journal articles | 2019
    Dietmann R; Ostafe A; Shparlinski IE, 2019, 'Discriminants of Fields Generated by Polynomials of Given Height', ,
    Journal articles | 2019
    Ostafe A; Young M, 2019, 'On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics', Transactions of the American Mathematical Society, 00,
    Journal articles | 2019
    Ostafe A, 2019, 'Polynomial values in affine subspaces of finite fields', Journal d'Analyse Mathematique, 138, pp. 49 - 81,
    Journal articles | 2018
    Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Orbits of Polynomial Dynamical Systems Modulo Primes', Proceedings of the American Mathematical Society, 146, pp. 2015 - 2025,
    Journal articles | 2018
    D’Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198,
    Journal articles | 2018
    Gómez-Pérez D; Nicolás AP; Ostafe A; Sadornil D, 2018, 'Stable polynomials over finite fields', Revista Matematica Iberoamericana, 30, pp. 523 - 535,
    Journal articles | 2018
    Gómez-Pérez D; Ostafe A; Sha M, 2018, 'The Arithmetic of Consecutive Polynomial Sequences over Finite Fields', Finite Fields and Their Applications, 50, pp. 35 - 65,
    Journal articles | 2018
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On abelian multiplicatively dependent points on a curve in a torus', The Quarterly Journal of Mathematics,
    Journal articles | 2018
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem', MICHIGAN MATHEMATICAL JOURNAL, 5,
    Journal articles | 2018
    Ostafe A; Sha M, 2018, 'Counting Dynamical Systems over Finite Fields', Contemporary Mathematics, pp. 187 - 203,
    Journal articles | 2018
    Ostafe A; Sha M, 2018, 'Counting dynamical systems over finite fields', Contemporary Mathematics, 669, pp. 187 - 203,
    Journal articles | 2018
    Ostafe A, 2018, 'On Some Extensions of the Ailon–Rudnick Theorem', Monatshefte für Mathematik, 181, pp. 451 - 471,
    Journal articles | 2016
    Gomez-Perez D; Gutierrez J; Ostafe A, 2016, 'Common composites of triangular polynomial systems and hash functions', JOURNAL OF SYMBOLIC COMPUTATION, 72, pp. 182 - 195,
    Journal articles | 2016
    Ostafe A; Sha M, 2016, 'Corrigendum to On the quantitative dynamical Mordell-Lang conjecture [J. Number Theory, 156, (2015), 161-182] DOI: 10.1016/j.jnt.2015.04.011', Journal of Number Theory, 164, pp. 433 - 437,
    Journal articles | 2016
    Ostafe A, 2016, 'On roots of unity in orbits of rational functions', Proceedings of the American Mathematical Society,
    Journal articles | 2015
    Ostafe A; Sha M, 2015, 'On the quantitative dynamical Mordell-Lang conjecture', Journal of Number Theory, 156, pp. 161 - 182,
    Journal articles | 2014
    Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550,
    Journal articles | 2014
    Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134,
    Journal articles | 2014
    Gómez-Pérez D; Ostafe A; Topuzoǧlu A, 2014, 'On the Carlitz rank of permutations ofFqand pseudorandom sequences', Journal of Complexity, 30, pp. 279 - 289,
    Journal articles | 2012
    Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369,
    Journal articles | 2012
    Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837,
    Journal articles | 2012
    Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 574, pp. 131 - 143,
    Journal articles | 2012
    Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33,
    Journal articles | 2012
    Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255,
    Journal articles | 2012
    Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, 28, pp. 238 - 249,
    Journal articles | 2012
    Ostafe A, 2012, 'Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems', Designs, Codes, and Cryptography, 63, pp. 59 - 72,
    Journal articles | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves,
    Journal articles | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, abs/1102.1053
    Journal articles | 2011
    Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, 7, pp. 1557 - 1571,
    Journal articles | 2011
    Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, 139, pp. 3815 - 3820,
    Journal articles | 2011
    Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, 25, pp. 50 - 71,
    Journal articles | 2011
    Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, 148, pp. 77 - 92,
    Journal articles | 2011
    Ostafe A, 2011, 'Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems', Designs, Codes, and Cryptography, pp. 1 - 14,
    Journal articles | 2010
    Chen Z; Ostafe A; Winterhof A, 2010, 'Structure of pseudorandom numbers derived from fermat quotients', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6087 LNCS, pp. 73 - 85,
    Journal articles | 2010
    Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, 23, pp. 501 - 513,
    Journal articles | 2010
    Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, 16, pp. 320 - 328,
    Journal articles | 2010
    Ostafe A; Shparlinski IE; Winterhof A, 2010, 'On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences', Advances in Mathematics of Communications, 4, pp. 369 - 379,
    Journal articles | 2010
    Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, 79, pp. 501 - 511,
    Journal articles | 2010
    Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, 138, pp. 2653 - 2656,
    Journal articles | 2010
    Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, 2, pp. 49 - 67,
    Journal articles | 2010
    Ostafe A, 2010, 'Multivariate permutation polynomial systems and nonlinear pseudorandom number generators', Finite Fields and their Applications, 16, pp. 144 - 154,
    Journal articles | 2010
    Ostafe A, 2010, 'Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6087 LNCS, pp. 62 - 72,
  • Preprints | 2024
    Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, Statistics of ranks, determinants and characteristic polynomials of rational matrices,
    Preprints | 2024
    Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials,
    Preprints | 2023
    Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups,
    Preprints | 2023
    Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems,
    Preprints | 2023
    Ostafe A; Shparlinski IE, 2023, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant,
    Preprints | 2022
    Ferraguti A; Ostafe A; Zannier U, 2022, Cyclotomic and abelian points in backward orbits of rational functions, ,
    Preprints | 2022
    Habegger P; Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices,
    Preprints | 2022
    Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups,
    Preprints | 2021
    Bérczes A; Bugeaud Y; Mello J; Ostafe A; Sha M, 2021, Multiplicative dependence of rational values modulo approximate finitely generated groups, ,
    Preprints | 2021
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions, ,
    Preprints | 2021
    Ostafe A; Shparlinski IE; Voloch JF, 2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, ,
    Preprints | 2021
    Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions, ,
    Preprints | 2020
    Barroero F; Capuano L; Mérai L; Ostafe A; Sha M, 2020, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes, ,
    Preprints | 2020
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic, ,
    Preprints | 2020
    Ostafe A; Shparlinski I, 2020, On the Skolem problem and some related questions for parametric families of linear recurrence sequences, ,
    Preprints | 2019
    Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height, ,
    Preprints | 2019
    Mérai L; Ostafe A; Shparlinski IE, 2019, Dynamical irreducibility of polynomials modulo primes, ,
    Preprints | 2019
    Ostafe A; Pottmeyer L; Shparlinski IE, 2019, Perfect powers in value sets and orbits of polynomials, ,
    Preprints | 2018
    Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2018, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups, ,
    Preprints | 2017
    Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2017, Orbits of Polynomial Dynamical Systems Modulo Primes, ,
    Preprints | 2017
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On abelian multiplicatively dependent points on a curve in a torus, ,
    Preprints | 2017
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem, ,
    Preprints | 2015
    D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2015, Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems, ,
    Preprints | 2015
    Gómez-Pérez D; Ostafe A; Sha M, 2015, The Arithmetic of Consecutive Polynomial Sequences over Finite Fields, ,
    Preprints | 2015
    Ostafe A; Sha M, 2015, Counting dynamical systems over finite fields, ,
    Preprints | 2015
    Ostafe A; Sha M, 2015, On the quantitative dynamical Mordell-Lang conjecture, ,
    Preprints | 2012
    Gomez-Perez D; Nicolas AP; Ostafe A; Sadornil D, 2012, Stable Polynomials over Finite Fields, ,
    Preprints | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, ,
    Preprints | 2011
    Ostafe A; Shparlinski I, 2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems, ,
    Conference Papers | 2011
    Ostafe A; Thomson D; Winterhof A, 2011, 'On the Waring Problem with multivariate Dickson polynomials', in Lavrauw M; Mullen GL; Nikova S; Panario D; Storme L (eds.), THEORY AND APPLICATIONS OF FINITE FIELDS, AMER MATHEMATICAL SOC, BELGIUM, Ghent, pp. 153 - +, presented at 10th International Conference on Finite Fields and Their Applications, BELGIUM, Ghent, 11 July 2011 - 15 July 2011,
    Preprints | 2010
    Ostafe A; Shparlinski IE, 2010, Pseudorandomness and Dynamics of Fermat Quotients, ,
    Preprints | 2009
    Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski I, 2009, Some Additive Combinatorics Problems in Matrix Rings, ,
    Preprints | 2009
    Ostafe A; Shparlinski I, 2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators, ,
    Preprints | 2009
    Ostafe A; Shparlinski IE, 2009, On the Length of Critical Orbits of Stable Quadratic Polynomials, ,
    Preprints | 2009
    Ostafe A; Shparlinski IE, 2009, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials, ,