By Professor Igor Shparlinski

Book Chapters

Shparlinski IE, 2002, 'EXPONENTIAL SUMS IN CODING THEORY, CRYPTOLOGY AND ALGORITHMS', in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, pp. 323 - 383, http://dx.doi.org/10.1142/9789812388841_0009

von zur Gathen J; Shparlinski I, 2001, 'Gauß Periods in Finite Fields', in Finite Fields and Applications, Springer Berlin Heidelberg, pp. 162 - 177, http://dx.doi.org/10.1007/978-3-642-56755-1_14

Friedlander JB; Lieman D; Shparlinski IE, 1999, 'On the Distribution of the RSA Generator', in Sequences and their Applications, Springer London, pp. 205 - 212, http://dx.doi.org/10.1007/978-1-4471-0551-0_14

Shparlinski I, 1996, 'Approximate constructions in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 313 - 332, http://dx.doi.org/10.1017/cbo9780511525988.024

Mullen GL; Shparlinski I, 1996, 'Open problems and conjectures in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 243 - 268, http://dx.doi.org/10.1017/cbo9780511525988.021

Shparlinski IE, 1995, 'On Some Characteristics of Uniformity of Distribution and Their Applications', in Computational Algebra and Number Theory, Springer Netherlands, pp. 227 - 241, http://dx.doi.org/10.1007/978-94-017-1108-1_16

Shparlinski IE, 'Diffie–Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 154 - 158, http://dx.doi.org/10.1007/0-387-23483-7_112

Edited Books

Shparlinski I; Brenner SC; Shu C-W; Szyld DB, (eds.), 2020, 75 Years of Mathematics of Computation, American Mathematical Society, https://bookstore.ams.org/conm-754

Journal articles

Shparlinski IE; Wijaya LP, 2025, 'On nonzero coefficients of binary cyclotomic polynomials', Journal of Number Theory, 271, pp. 246 - 258, http://dx.doi.org/10.1016/j.jnt.2024.11.008

Mérai L; Shparlinski IE, 2025, 'Number of characteristic polynomials of matrices with bounded height', Linear Algebra and Its Applications, 712, pp. 1 - 8, http://dx.doi.org/10.1016/j.laa.2025.02.012

GARAEV MZ; PARDO JC; SHPARLINSKI IE, 2025, 'BINARY AND TERNARY CONGRUENCES INVOLVING INTERVALS AND SETS MODULO A PRIME', Bulletin of the Australian Mathematical Society, pp. 1 - 11, http://dx.doi.org/10.1017/s0004972725000152

Shparlinski IE, 2025, 'Sums of multidimensional Kloosterman sums', Periodica Mathematica Hungarica, 90, pp. 1 - 6, http://dx.doi.org/10.1007/s10998-024-00606-0

Perucca A; Shparlinski IE, 2025, 'Uniform bounds for the density in Artin's conjecture on primitive roots', Bulletin of the London Mathematical Society, 57, pp. 978 - 991, http://dx.doi.org/10.1112/blms.70011

Bulinski K; Shparlinski IE, 2024, 'Counting elements of the congruence subgroup', Canadian Mathematical Bulletin, 67, pp. 955 - 969, http://dx.doi.org/10.4153/S0008439524000365

Mohammadi A; Ostafe A; Shparlinski IE, 2024, 'On some matrix counting problems', Journal of the London Mathematical Society, 110, http://dx.doi.org/10.1112/jlms.70044

Garaev MZ; Rudnick Z; Shparlinski IE, 2024, 'On a family of sparse exponential sums', Mathematische Nachrichten, 297, pp. 4214 - 4231, http://dx.doi.org/10.1002/mana.202300426

Garaev MZ; Shparlinski IE, 2024, 'On some congruences and exponential sums', Finite Fields and their Applications, 98, http://dx.doi.org/10.1016/j.ffa.2024.102451

Browning TD; Shparlinski IE, 2024, 'Square-free values of random polynomials', Journal of Number Theory, 261, pp. 220 - 240, http://dx.doi.org/10.1016/j.jnt.2024.02.013

Shparlinski IE, 2024, 'ON QUADRATIC FIELDS GENERATED BY POLYNOMIALS', Bulletin of the Australian Mathematical Society, 109, pp. 476 - 485, http://dx.doi.org/10.1017/S0004972723000606

Shparlinski IE, 2024, 'Rational numbers with small denominators in short intervals', Archiv der Mathematik, 122, pp. 629 - 637, http://dx.doi.org/10.1007/s00013-024-01993-z

Kerr B; Mello J; Shparlinski IE, 2024, 'An effective local-global principle and additive combinatorics in finite fields', Journal d'Analyse Mathematique, 152, pp. 109 - 135, http://dx.doi.org/10.1007/s11854-023-0291-2

Mérai L; Shparlinski IE; Winterhof A, 2024, 'Character sums over sparse elements of finite fields', Bulletin of the London Mathematical Society, 56, pp. 1488 - 1510, http://dx.doi.org/10.1112/blms.13008

Dietmann R; Ostafe A; Shparlinski IE, 2024, 'Discriminants of fields generated by polynomials of given height', Israel Journal of Mathematics, 260, pp. 73 - 103, http://dx.doi.org/10.1007/s11856-023-2557-x

Dubickas A; Sha M; Shparlinski IE, 2024, 'Euclidean minima of algebraic number fields', Archiv der Mathematik, 122, pp. 405 - 414, http://dx.doi.org/10.1007/s00013-023-01943-1

Hauck M; Shparlinski IE, 2024, 'Smooth numbers with few nonzero binary digits', Canadian Mathematical Bulletin, 67, pp. 74 - 89, http://dx.doi.org/10.4153/S0008439523000504

Borda B; Munsch M; Shparlinski IE, 2024, 'Pointwise and correlation bounds on Dedekind sums over small subgroups', Research in Number Theory, 10, pp. 28 - 28, http://dx.doi.org/10.1007/s40993-024-00514-9

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, http://dx.doi.org/10.2422/2036-2145.202307_011

Baker RC; Chen C; Shparlinski IE, 2024, 'Bounds on the norms of maximal operators on Weyl sums', Journal of Number Theory, 256, pp. 329 - 353, http://dx.doi.org/10.1016/j.jnt.2023.10.001

Shkredov ID; Shparlinski IE; Zaharescu A, 2024, 'On the distribution of modular square roots of primes', Mathematische Zeitschrift, 306, http://dx.doi.org/10.1007/s00209-024-03436-5

Dartyge C; Martin B; Rivat J; Shparlinski IE; Swaenepoel C, 2024, 'Reversible primes', Journal of the London Mathematical Society, 109, http://dx.doi.org/10.1112/jlms.12883

Shparlinski IE; Thuswaldner JM, 2024, 'Weyl Sums over Integers with Digital Restrictions', Michigan Mathematical Journal, 74, pp. 189 - 214, http://dx.doi.org/10.1307/mmj/20216094

Dartyge C; Martin B; Rivat J; Shparlinski IE; Swaenepoel C, 2024, 'Reversible primes', Journal of the London Mathematical Society, 109, pp. 1 - 38, http://dx.doi.org/10.1112/jlms.12883

Ostafe A; Shparlinski IE; Voloch JF, 2024, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, 176, pp. 39 - 53, http://dx.doi.org/10.1017/S0305004123000415

Kerr B; Mohammad A; Shparlinski IE, 2024, 'ADDITIVE ENERGY OF POLYNOMIAL IMAGES', SIAM Journal on Discrete Mathematics, 38, pp. 2163 - 2180, http://dx.doi.org/10.1137/23M1582941

El Abdalaoui H; Shparlinski IE; Steiner RS, 2024, 'Chowla and Sarnak conjectures for Kloosterman sums', Mathematische Nachrichten, 297, pp. 209 - 228, http://dx.doi.org/10.1002/mana.202200480

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2024, 'ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS', Journal of the Institute of Mathematics of Jussieu, http://dx.doi.org/10.1017/S1474748023000397

Brandes J; Chen C; Shparlinski I, 2024, 'Local mean value estimates for Weyl sums', Revista Matematica Iberoamericana, 40, pp. 2095 - 2134, http://dx.doi.org/10.4171/RMI/1495

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, 'Statistics of ranks, determinants and characteristic polynomials of rational matrices', Forum Mathematicum, http://dx.doi.org/10.1515/forum-2024-0114

Iyer S; Shparlinski IE, 2024, 'Character sums over elements of extensions of finite fields with restricted coordinates', Finite Fields and Their Applications, 93, pp. 102335 - 102335, http://dx.doi.org/10.1016/j.ffa.2023.102335

Fouvry É; Shparlinski IE, 2023, 'On character sums with determinants', Science China Mathematics, 66, pp. 2693 - 2714, http://dx.doi.org/10.1007/s11425-022-2122-0

Mérai L; Shparlinski IE, 2023, 'DISTRIBUTION OF RECURSIVE MATRIX PSEUDORANDOM NUMBER GENERATOR MODULO PRIME POWERS', Mathematics of Computation, 93, pp. 1355 - 1370, http://dx.doi.org/10.1090/mcom/3895

Garaev MZ; Shparlinski IE, 2023, 'On the distribution of modular inverses from short intervals', Mathematika, 69, pp. 1183 - 1194, http://dx.doi.org/10.1112/mtk.12224

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2023, 'FUNCTIONAL GRAPHS OF FAMILIES OF QUADRATIC POLYNOMIALS', Mathematics of Computation, 92, pp. 2307 - 2331, http://dx.doi.org/10.1090/mcom/3838

Shparlinski IE, 2023, 'On the number of Diophantine m-tuples in finite fields', Finite Fields and their Applications, 90, pp. 102241, http://dx.doi.org/10.1016/j.ffa.2023.102241

Kerr B; Shparlinski IE; Wu X; Xi P, 2023, 'Bounds on bilinear forms with Kloosterman sums', Journal of the London Mathematical Society, 108, pp. 578 - 621, http://dx.doi.org/10.1112/jlms.12753

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, http://dx.doi.org/10.1093/imrn/rnac226

Shparlinski IE, 2023, 'Fixed points of the subset sum pseudorandom number generators', Designs, Codes, and Cryptography, 91, pp. 2473 - 2479, http://dx.doi.org/10.1007/s10623-023-01209-5

Dąbrowski A; Pomykała J; Shparlinski IE, 2023, 'On oracle factoring of integers', Journal of Complexity, 76, http://dx.doi.org/10.1016/j.jco.2023.101741

Kaminski M; Shparlinski IE; Waldschmidt M, 2023, 'On sets of linear forms of maximal complexity', Computational Complexity, 32, http://dx.doi.org/10.1007/s00037-022-00234-5

Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, 385, pp. 309 - 355, http://dx.doi.org/10.1007/s00208-021-02352-x

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