By Professor Igor Shparlinski

Conference Papers

Gathen JVZ; Shparlinski I, 1998, 'The crew pram complexity of modular inversion', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 305 - 315

von zur Gathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields extended abstract', in Annual Symposium on Foundations of Computer Science - Proceedings, pp. 284 - 292

vonzurGathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields', in 36TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS, I E E E, COMPUTER SOC PRESS, WI, MILWAUKEE, pp. 284 - 292, presented at 36th Annual Symposium on Foundations of Computer Science (FOCS 95), WI, MILWAUKEE, 23 October 1995 - 25 October 1995, http://dx.doi.org/10.1109/SFCS.1995.492484

von zur Gathen J; Shparlinski I, 1995, 'Orders of gauss periods in finite fields', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 208 - 215, http://dx.doi.org/10.1007/bfb0015425

van der Poorten AJ; Shparlinski I; Zimmer HG, 1995, 'Number Theoretic and Algebraic Methods in Computer Science', in Number Theoretic and Algebraic Methods in Computer Science, WORLD SCIENTIFIC, pp. 1 - 214, presented at International Conference on NTAMCS '93, http://dx.doi.org/10.1142/9789814532532

Von Zur Gathen J; Shparlinski I, 1994, 'Components and projections of curves over finite fields', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 297 - 305, http://dx.doi.org/10.1007/3-540-58325-4_193

Shparlinski IE, 1994, 'On some applications of finitely generated semi-groups', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 265 - 279, http://dx.doi.org/10.1007/3-540-58691-1_66

Von Zur Gathen J; Karpinski M; Shparlinski I, 1993, 'Counting curves and their projections', in Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 805 - 812, http://dx.doi.org/10.1145/167088.167292

Shparlinski IE, 1992, 'On Gaussian sums for finite fields and elliptic curves', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 5 - 15, http://dx.doi.org/10.1007/bfb0034335

STEPANOV SA; SHPARLINSKI IE, 1991, 'ON NORMAL BASES OF ALGEBRAIC NUMBER-FIELDS', in Schweiger F; Manstavicius E (ed.), NEW TRENDS IN PROBABILITY AND STATISTICS, VOL 2, VSP BV, LITHUANIA, PALANGA, pp. 369 - 378, presented at INTERNATIONAL CONF ON ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY, IN HONOUR OF JONAS KUBILIUS ON THE OCCASION OF HIS 70TH BIRTHDAY, LITHUANIA, PALANGA, 24 September 1991 - 28 September 1991, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992BY41L00033&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1991, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', in Stichtenoth H; Tsfasman MA (ed.), CODING THEORY AND ALGEBRAIC GEOMETRY, SPRINGER-VERLAG BERLIN, FRANCE, CTR INT RENCONTRES MATH, LUMINY, pp. 145 - 169, presented at WORKSHOP ON ALGEBRAIC GEOMETRY AND CODING THEORY - 3 ( AGCT-3 ), FRANCE, CTR INT RENCONTRES MATH, LUMINY, 17 June 1991 - 21 June 1991, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992BX67L00014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Stepanov SA; Shparlinskiy IE, 1987, 'On structure complexity of normal basis of finite field', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 414 - 416, http://dx.doi.org/10.1007/3-540-18740-5_90

Working Papers

Chen C; Shparlinski IE, 2021, Restricted Mean Value Theorems and the Metric Theory of Restricted Weyl Sums, http://dx.doi.org10.1093/qmath/haaa052

Chen C; Shparlinski IE, 2021, On a hybrid version of the Vinogradov mean value theorem, http://dx.doi.org10.1007/s10474-020-01111-9

Munsch M; Shparlinski IE, 2020, On smooth square-free numbers in arithmetic progressions, http://dx.doi.org10.1112/jlms.12297

Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, http://dx.doi.org10.1307/mmj/1573700737

Banks WD; Shparlinski IE, 2020, Sums with the Möbius function twisted by characters with powerful moduli, http://dx.doi.org10.1090/tran/7914

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, http://dx.doi.org, http://arxiv.org/abs/1912.00345v4

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, http://dx.doi.org, http://arxiv.org/abs/1711.05335v2

Preprints

Ostafe A; Shparlinski IE, 2025, Counting integer matrices with square-free determinants, http://arxiv.org/abs/2503.13768v1

Koh D; Shparlinski IE, 2025, Mean value theorems for rational exponential sums, http://arxiv.org/abs/2503.10933v1

Ostafe A; Pomerance C; Shparlinski IE, 2025, Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros, http://arxiv.org/abs/2503.03985v1

Manning A; Ostafe A; Shparlinski IE, 2025, Counting matrices over finite rank multiplicative groups, http://arxiv.org/abs/2502.07100v1

Bérczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in linear recurrence sequences, http://arxiv.org/abs/2501.17365v1

Klurman O; Shparlinski IE; Teräväinen J, 2024, On Artin's conjecture on average and short character sums, http://arxiv.org/abs/2412.13355v1

Bhakta S; Shparlinski I, 2024, Exponential Sums with Sparse Polynomials and Distribution of the Power Generator, http://arxiv.org/abs/2412.07989v2

Blomer V; Risager MS; Shparlinski IE, 2024, Triple sums of Kloosterman sums and the discrepancy of modular inverses, http://arxiv.org/abs/2411.17823v2

Shao X; Shparlinski IE; Wijaya LP, 2024, Sums of Kloosterman sums over square-free and smooth integers, http://arxiv.org/abs/2411.12113v1

Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2024, On quantum ergodicity for higher dimensional cat maps, http://arxiv.org/abs/2411.05997v1

Shparlinski IE; Voloch JF, 2024, On the Waring problem with Dickson polynomials modulo a prime, http://arxiv.org/abs/2410.08732v1

Garaev MZ; Pardo JC; Shparlinski IE, 2024, Binary and ternary congruences involving intervals and sets modulo a prime, http://dx.doi.org/10.1017/S0004972725000152

Shkredov ID; Shparlinski IE, 2024, On the determinants of matrices with elements from arbitrary sets, http://arxiv.org/abs/2408.04350v1

Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials, http://arxiv.org/abs/2407.20464v1

Shparlinski IE, 2024, Exponential sums over integers without large prime divisors, http://arxiv.org/abs/2404.10278v1

Fouvry É; Shparlinski IE; Xi P, 2024, Estimates for trilinear and quadrilinear character sums, http://arxiv.org/abs/2404.09295v4

Perucca A; Shparlinski IE, 2024, Uniform bounds for the density in Artin's conjecture on primitive roots, http://arxiv.org/abs/2401.11589v1

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, Statistics of ranks, determinants and characteristic polynomials of rational matrices, http://arxiv.org/abs/2401.10086v2

Iyer S; Shparlinski I, 2024, Character sums over elements of extensions of finite fields with restricted coordinates

Ostafe A; Shparlinski IE, 2023, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant, http://arxiv.org/abs/2312.12626v2

Shparlinski IE, 2023, Rational numbers with small denominators in short intervals, http://arxiv.org/abs/2311.16640v2

Baird R; Kerr B; Shparlinski I, 2023, Bohr sets generated by polynomials and Coppersmith's method in many variables, http://arxiv.org/abs/2310.20342v1

Mérai L; Shparlinski IE, 2023, Number of characteristic polynomials of matrices with bounded height, http://arxiv.org/abs/2310.09052v2

Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems, http://arxiv.org/abs/2310.05038v2

Garaev M; Rudnick Z; Shparlinski I, 2023, On a family of sparse exponential sums, http://arxiv.org/abs/2309.11887v1

Munsch M; Shparlinski IE, 2023, Moments and non-vanishing of $L$-functions over thin subgroups, http://arxiv.org/abs/2309.10207v3

Bulinski K; Shparlinski IE, 2023, Counting elements of the congruence subgroup, http://dx.doi.org/10.4153/S0008439524000365

Dubickas A; Sha M; Shparlinski IE, 2023, Euclidean minima of algebraic number fields, http://arxiv.org/abs/2307.10880v1

Shparlinski IE; Wijaya LP, 2023, On Nonzero Coefficients of Binary Cyclotomic Polynomials, http://arxiv.org/abs/2307.07229v2

Kerr B; Mohammadi A; Shparlinski IE, 2023, Additive energy of polynomial images, http://arxiv.org/abs/2306.10677v1

Browning T; Shparlinski I, 2023, Square-free values of random polynomials, http://arxiv.org/abs/2305.15493v1

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