By Professor Igor Shparlinski

Journal articles

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

Mérai L; Shparlinski I, 2023, 'Distribution of recursive matrix pseudorandom number generator modulo prime powers', Mathematics of Computation, 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, 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, pp. 101741 - 101741, 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

Kerr B; Mello J; Shparlinski IE, 2023, 'An effective local-global principle and additive combinatorics in finite fields', Journal d'Analyse Mathematique, pp. 1 - 27, http://dx.doi.org/10.1007/s11854-023-0291-2

Bag N; Shparlinski IE, 2023, 'Bounds on bilinear sums of Kloosterman sums', Journal of Number Theory, 242, pp. 102 - 111, http://dx.doi.org/10.1016/j.jnt.2022.07.006

Abdalaoui E; Shparlinski IE; Steiner RS, 2023, 'Chowla and Sarnak conjectures for Kloosterman sums', Mathematische Nachrichten, http://dx.doi.org/10.1002/mana.202200480

Dietmann R; Ostafe A; Shparlinski IE, 2023, 'Discriminants of fields generated by polynomials of given height', Israel Journal of Mathematics, http://dx.doi.org/10.1007/s11856-023-2557-x

Chen C; Shparlinski IE, 2023, 'Hybrid Bounds on Two-Parametric Families of Weyl Sums Along Smooth Curves', Michigan Mathematical Journal, 73, pp. 123 - 139, http://dx.doi.org/10.1307/MMJ/20205904

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

Shparlinski IE, 2023, 'On Quadratic Fields Generated by Polynomials', Bulletin of the Australian Mathematical Society, pp. 1 - 10, http://dx.doi.org/10.1017/S0004972723000606

Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2023, 'On the distribution of multiplicatively dependent vectors', Mathematical Research Letters, 30, pp. 509 - 540, http://dx.doi.org/10.4310/MRL.2023.v30.n2.a7

Shparlinski IE, 2023, 'On the Glasner property for matrices with polynomial entries', Journal of Number Theory, 242, pp. 522 - 531, http://dx.doi.org/10.1016/j.jnt.2022.04.015

Hauck M; Shparlinski IE, 2023, 'Smooth numbers with few non-zero binary digits', Canadian Mathematical Bulletin, pp. 1 - 16, http://dx.doi.org/10.4153/S0008439523000504

Brandes J; Shparlinski IE, 2023, 'Two-dimensional Weyl sums failing square-root cancellation along lines', Arkiv for Matematik, 61, pp. 267 - 276, http://dx.doi.org/10.4310/ARKIV.2023.v61.n2.a1

Ostafe ALINA; Shparlinski IE; Voloch JF, 2023, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, pp. 1 - 15, http://dx.doi.org/10.1017/S0305004123000415

Shparlinski IE; Thuswaldner JM, 2023, 'Weyl Sums over Integers with Digital Restrictions', Michigan Mathematical Journal, -1, http://dx.doi.org/10.1307/mmj/20216094

Baker RC; Chen C; Shparlinski IE, 2023, 'Bounds on the Norms of Maximal Operators on Weyl Sums', Journal of Number Theory, http://dx.doi.org/10.1016/j.jnt.2023.10.001

Shkredov ID; Shparlinski IE; Zaharescu A, 2022, 'Bilinear Forms with Modular Square Roots and Twisted Second Moments of Half Integral Weight Dirichlet Series', International Mathematics Research Notices, 2022, pp. 17431 - 17474, http://dx.doi.org/10.1093/imrn/rnab220

Bagshaw C; Shparlinski IE, 2022, 'Energy bounds, bilinear forms and their applications in function fields', Finite Fields and their Applications, 82, pp. 102048 - 102048, http://dx.doi.org/10.1016/j.ffa.2022.102048

Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics

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, http://dx.doi.org/10.4153/S0008414X21000080

Baker RC; Munsch M; Shparlinski IE, 2022, 'Additive energy and a large sieve inequality for sparse sequences', Mathematika, 68, pp. 362 - 399, http://dx.doi.org/10.1112/mtk.12140

Ghioca D; Shparlinski IE, 2022, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, 233, pp. 112 - 125, http://dx.doi.org/10.1016/j.jnt.2021.06.006

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 1 - 46, http://dx.doi.org/10.1016/j.jmaa.2022.126030

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, http://dx.doi.org/10.1112/jlms.12554

Banks W; Shparlinski I, 2022, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, 54, pp. 301 - 317, http://dx.doi.org/10.1112/blms.12524

Shparlinski IE, 2022, 'Bilinear sums of Gauss sums', Acta Arithmetica, 202, pp. 379 - 388, http://dx.doi.org/10.4064/aa210523-3-2

Shparlinski IE, 2022, 'MULTIPLICATIVE PROPERTIES of HILBERT CUBES', SIAM Journal on Discrete Mathematics, 36, pp. 1064 - 1070, http://dx.doi.org/10.1137/22M1470396

Kerr B; Mérai L; Shparlinski IE, 2022, 'On digits of Mersenne numbers', Revista Matematica Iberoamericana, 38, pp. 1901 - 1925, http://dx.doi.org/10.4171/RMI/1316

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 126030 - 126030, http://dx.doi.org/10.1016/j.jmaa.2022.126030

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, http://dx.doi.org/10.1017/S0004972721000083

Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv der Mathematik, 117, pp. 261 - 266, http://dx.doi.org/10.1007/s00013-021-01623-y

Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2

Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5

Baker RC; Chen C; Shparlinski IE, 2021, 'Bounds on the Norms of Maximal Operators on Weyl Sums', , http://arxiv.org/abs/2107.13674v1

Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, 64, http://dx.doi.org/10.1016/j.jco.2020.101542

Shparlinski IE; Thuswaldner JM, 2021, 'Weyl sums over integers with digital restrictions', , http://arxiv.org/abs/2105.04835v1

Baker RC; Munsch M; Shparlinski IE, 2021, 'Additive energy and a large sieve inequality for sparse sequences', , http://arxiv.org/abs/2103.12659v2

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, 'Energy bounds for modular roots and their applications', , http://arxiv.org/abs/2103.09405v1

Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743

Sha M; Shparlinski IE, 2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363

Mérai L; Shparlinski IE, 2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, 8, http://dx.doi.org/10.1007/s40687-021-00249-4

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