By Professor Igor Shparlinski

Conference Papers

Hoffstein J; Lieman D, 1999, 'The distribution of the quadratic symbol in function fields and a faster mathematical stream cipher', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 59 - 68, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

van der Poorten A, 1999, 'The Hermite-Serret algorithm and 12(2)+33(2)', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 129 - 136, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

von zur Gathen J; Shparlinski I, 1999, 'Gauss periods in finite fields', in Jungnickel D; Niederreiter H (ed.), FINITE FIELDS AND APPLICATIONS, SPRINGER-VERLAG BERLIN, GERMANY, UNIV AUGSBURG, DEPT MATH, AUGSBURG, pp. 162 - 177, presented at 5th International Conference on Finite Fields and Applications, GERMANY, UNIV AUGSBURG, DEPT MATH, AUGSBURG, 02 August 1999 - 06 August 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169087900014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Bernasconi A; Shparlinski I, 1999, 'Circuit complexity of testing square-free numbers', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 47 - 56, http://dx.doi.org/10.1007/3-540-49116-3_4

Von Zur Gathen J; Shparlinski I, 1999, 'Constructing elements of large order in finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 404 - 409, http://dx.doi.org/10.1007/3-540-46796-3_38

Allender E; Saks M; Shparlinski I, 1999, 'Lower bound for primality', in Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 10 - 14

Cai JY; Havas G; Mans B; Nerurkar A; Seifert JP; Shparlinski I, 1999, 'On routing in circulant graphs', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 360 - 369, http://dx.doi.org/10.1007/3-540-48686-0_36

Bernasconi A; Damm C; Shparlinski IE, 1999, 'On the average sensitivity of testing square-free numbers', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 291 - 299, http://dx.doi.org/10.1007/3-540-48686-0_29

Karpinski M; Shparlinski I, 1999, 'On the computational hardness of testing square-freeness of sparse polynomials', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 492 - 497, http://dx.doi.org/10.1007/3-540-46796-3_47

Griffin F; Niederreiter H; Shparlinski IE, 1999, 'On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 87 - 93, http://dx.doi.org/10.1007/3-540-46796-3_9

Griffin F; Shparlinski IE, 1999, 'On the linear complexity of the naor—reingold pseudo-random function', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 301 - 308, http://dx.doi.org/10.1007/978-3-540-47942-0_25

Grant D; Krastev K; Lieman D; Shparlinski I, 1998, 'A public key cryptosystem based on sparse polynomials', in Buchmann J; Hoholdt T; Stichtenoth H; TapiaRecillas H (eds.), CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS, SPRINGER-VERLAG BERLIN, MEXICO, GUANAJUATO, pp. 114 - 121, presented at International Conference on Coding Theory, Cryptography and Related Areas, MEXICO, GUANAJUATO, 20 April 1998 - 24 April 1998, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000085321900010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Mans B; Pappalardi F; Shparlinski I, 1998, 'On the ádám conjecture on circulant graphs', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 251 - 260, http://dx.doi.org/10.1007/3-540-68535-9_29

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://dx.doi.org/10.4153/S0008439525000475

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/2411.05997v2

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

Drappeau S; Shparlinski IE, 2024, Exponential sums over integers without large prime divisors, http://arxiv.org/abs/2404.10278v2

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

Back to profile page