By Professor Igor Shparlinski

Preprints

Ostafe A; Shparlinski I, 2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems, http://dx.doi.org/10.48550/arxiv.1109.0575

Shparlinski IE, 2011, Fermat quotients: Exponential sums, value set and primitive roots, http://dx.doi.org/10.48550/arxiv.1104.3909

Shparlinski IE, 2011, On vanishing Fermat quotients and a bound of the Ihara sum, http://dx.doi.org/10.48550/arxiv.1104.3910

Shparlinski IE, 2011, Modular Hyperbolas, http://dx.doi.org/10.48550/arxiv.1103.2879

Bourgain J; Konyagin S; Shparlinski I, 2011, Distribution on elements of cosets of small subgroups and applications, http://dx.doi.org/10.48550/arxiv.1103.0567

Bourgain J; Konyagin SV; Shparlinski IE, 2011, Distribution of Elements of Cosets of Small Subgroups and Applications

Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, http://arxiv.org/abs/1102.1053v1

Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, http://dx.doi.org/10.48550/arxiv.1102.1053

Konyagin SV; Shparlinski IE, 2010, On the Convex Hull of the Points on Modular Hyperbolas, http://arxiv.org/abs/1012.1444v2

Gonzalez JJA; Luca F; Pomerance C; Shparlinski I, 2010, On numbers $n$ dividing the $n$th term of a linear recurrence, http://dx.doi.org/10.48550/arxiv.1010.4544

Farashahi RR; Shparlinski IE, 2010, On Pseudopoints of Algebraic Curves, http://dx.doi.org/10.48550/arxiv.1005.4775

Farashahi RR; Shparlinski IE, 2010, Pseudorandom Bits From Points on Elliptic Curves, http://dx.doi.org/10.48550/arxiv.1005.4771

Shparlinski I, 2010, On Small Solutions to Quadratic Congruences, http://dx.doi.org/10.48550/arxiv.1004.0715

Shparlinski IE, 2010, On the Restricted Divisor Function in Arithmetic Progressions, http://dx.doi.org/10.48550/arxiv.1003.5347

Farashahi RR; Shparlinski IE, 2010, On group structures realized by elliptic curves over a fixed finite field, http://arxiv.org/abs/1003.3000v1

Banks WD; Pappalardi F; Shparlinski IE, 2010, On group structures realized by elliptic curves over arbitrary finite fields, http://dx.doi.org/10.48550/arxiv.1003.3004

Balog A; Broughan KA; Shparlinski IE, 2010, On the Number of Solutions of Exponential Congruences, http://dx.doi.org/10.48550/arxiv.1003.1997

Ostafe A; Shparlinski IE, 2010, Pseudorandomness and Dynamics of Fermat Quotients, http://dx.doi.org/10.48550/arxiv.1001.1504

Shparlinski IE; Stange KE, 2009, Character sums with division polynomials, http://dx.doi.org/10.48550/arxiv.0912.5246

Ostafe A; Shparlinski IE, 2009, On the Length of Critical Orbits of Stable Quadratic Polynomials, http://dx.doi.org/10.48550/arxiv.0909.3972

Ostafe A; Shparlinski IE, 2009, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials, http://dx.doi.org/10.48550/arxiv.0908.4519

Glebsky L; Shparlinski IE, 2009, Short Cycles in Repeated Exponentiation Modulo a Prime, http://dx.doi.org/10.48550/arxiv.0908.3920

Ahmadi O; Shparlinski IE, 2009, On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields, http://dx.doi.org/10.48550/arxiv.0907.3664

Pomerance C; Shparlinski IE, 2009, Rank statistics for a family of elliptic curves over a function field, http://dx.doi.org/10.48550/arxiv.0903.2866

Shparlinski IE, 2009, On Point Sets in Vector Spaces over Finite Fields That Determine Only Acute Angle Triangles, http://dx.doi.org/10.48550/arxiv.0903.2520

Ostafe A; Shparlinski I, 2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators, http://dx.doi.org/10.48550/arxiv.0902.3884

Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski I, 2009, Some Additive Combinatorics Problems in Matrix Rings, http://dx.doi.org/10.48550/arxiv.0902.3482

Shparlinski IE, 2008, On Quadratic Fields Generated by Discriminants of Irreducible Trinomials, http://dx.doi.org/10.48550/arxiv.0811.1300

Naccache D; Shparlinski IE, 2008, Divisibility, Smoothness and Cryptographic Applications, http://arxiv.org/abs/0810.2067v3

Loiperdinger SS; Shparlinski IE, 2008, On the Distribution of the Euler Function of Shifted Smooth Numbers, http://dx.doi.org/10.48550/arxiv.0810.1093

Ahmadi O; Shparlinski I, 2008, On the Sum-Product Problem on Elliptic Curves, http://dx.doi.org/10.48550/arxiv.0806.0640

van Dam W; Shparlinski IE, 2008, Classical and Quantum Algorithms for Exponential Congruences, http://dx.doi.org/10.48550/arxiv.0804.1109

Shparlinski IE, 2008, On a Generalised Lehmer Problem for Arbitrary Powers, http://arxiv.org/abs/0803.3487v2

Shparlinski I, 2008, On Some Weighted Average Values of L-functions, http://dx.doi.org/10.48550/arxiv.0802.2378

Pomerance C; Shparlinski IE, 2007, On Pseudosquares and Pseudopowers, http://arxiv.org/abs/0712.1081v2

Konyagin SV; Pomerance C; Shparlinski IE, 2007, On the Distribution of Pseudopowers, http://dx.doi.org/10.48550/arxiv.0712.1080

Khan MR; Shparlinski IE; Yankov CL, 2007, On the Convex Closure of the Graph of Modular Inversions, http://dx.doi.org/10.48550/arxiv.0711.4100

Shparlinski IE, 2007, Arithmetic and Geometric Progressions in Productsets over Finite Fields, http://dx.doi.org/10.48550/arxiv.0711.1800

Graham SW; Shparlinski IE, 2007, On RSA Moduli with Almost Half of the Bits Prescribed, http://dx.doi.org/10.48550/arxiv.0709.2704

Shparlinski IE, 2007, On The Solvability of Bilinear Equations in Finite Fields, http://dx.doi.org/10.48550/arxiv.0708.2130

Friedlander JB; Kurlberg P; Shparlinski IE, 2007, Products in Residue Classes, http://dx.doi.org/10.48550/arxiv.0708.1562

Banks WD; Shparlinski IE, 2007, Prime numbers with Beatty sequences, http://arxiv.org/abs/0708.1015v1

Ahmadi O; Shparlinski IE; Voloch JF, 2007, Multiplicative Order of Gauss Periods, http://dx.doi.org/10.48550/arxiv.0707.4034

Shparlinski IE, 2007, Approximation by Several Rationals, http://dx.doi.org/10.48550/arxiv.0707.3371

Shparlinski IE, 2007, Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves, http://dx.doi.org/10.48550/arxiv.0707.2976

Cojocaru AC; Shparlinski IE, 2007, Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average, http://dx.doi.org/10.48550/arxiv.0705.3861

Shparlinski IE; Voloch JF, 2007, Visible Points on Curves over Finite Fields, http://arxiv.org/abs/0704.2446v1

Ford K; Luca F; Shparlinski IE, 2007, On the largest prime factor of the Mersenne numbers, http://dx.doi.org/10.48550/arxiv.0704.1327

Saxena N; Severini S; Shparlinski I, 2007, Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics, http://dx.doi.org/10.48550/arxiv.quant-ph/0703236

Banks WD; Shparlinski IE, 2006, Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height, http://dx.doi.org/10.48550/arxiv.math/0609144

Back to profile page