By Professor Igor Shparlinski

Journal articles

Bretèche RDL; Kurlberg P; Shparlinski IE, 2019, 'On the number of products which form perfect powers and discriminants of multiquadratic extensions', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz316

Shparlinski I, 2019, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, 15, pp. 469 - 477, http://dx.doi.org/10.1142/S1793042119500246

Karpinski M; Mérai L; Shparlinski IE, 2018, 'Identity testing and interpolation from high powers of polynomials of large degree over finite fields', Journal of Complexity, 49, pp. 74 - 84, http://dx.doi.org/10.1016/j.jco.2018.07.006

Shparlinski IE, 2018, 'On the Győry-Sárközy-Stewart conjecture in function fields', Czechoslovak Mathematical Journal, 68, pp. 1067 - 1077, http://dx.doi.org/10.21136/CMJ.2018.0085-17

Shparlinski IE, 2018, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, pp. 1 - 9, http://dx.doi.org/10.1142/S1793042119500246

Shparlinski IE, 2018, 'On Constructing Primitive Roots in Finite Fields With Advice', IEEE Transactions on Information Theory, 64, pp. 7132 - 7136, http://dx.doi.org/10.1109/TIT.2018.2810938

Shparlinski IE, 2018, 'Trilinear forms with double Kloosterman sums', International Journal of Number Theory, 14, pp. 2195 - 2203, http://dx.doi.org/10.1142/S1793042118501312

Liu K; Shparlinski IE; Zhang T, 2018, 'Bilinear forms with exponential sums with binomials', Journal of Number Theory, 188, pp. 172 - 185, http://dx.doi.org/10.1016/j.jnt.2017.12.011

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem', MICHIGAN MATHEMATICAL JOURNAL, 5, https://arxiv.org/abs/1706.05874

Shparlinski IE, 2018, 'Linear equations with rational fractions of bounded height and stochastic matrices', Quarterly Journal of Mathematics, 69, pp. 487 - 499, http://dx.doi.org/10.1093/qmath/hax049

Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212

D’Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437

Shparlinski IE, 2018, 'Character sums with smooth numbers', Archiv der Mathematik, 110, pp. 467 - 476, http://dx.doi.org/10.1007/s00013-018-1168-y

Shparlinski IE, 2018, 'Multiplicative orders in orbits of polynomials over finite fields', Glasgow Mathematical Journal, 60, pp. 487 - 493, http://dx.doi.org/10.1017/S0017089517000222

LUCA F; RADZIWIŁŁ M; SHPARLINSKI IE, 2018, 'On the typical size and cancellations among the coefficients of some modular forms', Mathematical Proceedings of the Cambridge Philosophical Society, 166, pp. 173 - 189, http://dx.doi.org/10.1017/S0305004117000780

Gómez-Pérez D; Shparlinski IE, 2018, 'Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions', Experimental Mathematics, 27, pp. 184 - 192, http://dx.doi.org/10.1080/10586458.2016.1239146

Shparlinski IE, 2018, 'Constructing Dominating Sets in Circulant Graphs', Annals of Combinatorics, 22, pp. 201 - 211, http://dx.doi.org/10.1007/s00026-018-0377-1

Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, 459, pp. 53 - 81, http://dx.doi.org/10.1016/j.jmaa.2017.10.070

Liu K; Shparlinski IE; Zhang T, 2018, 'Divisor problem in arithmetic progressions modulo a prime power', Advances in Mathematics, 325, pp. 459 - 481, http://dx.doi.org/10.1016/j.aim.2017.12.006

Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski IE, 2018, 'Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields', Algorithmica, 80, pp. 560 - 575, http://dx.doi.org/10.1007/s00453-016-0273-1

Shparlinski IE; Winterhof A, 2018, 'Codes correcting restricted errors', Designs, Codes, and Cryptography, http://dx.doi.org/10.1007/s10623-018-0585-z

Bordellès O; Luca F; Moree P; Shparlinski IE, 2018, 'DENOMINATORS of BERNOULLI POLYNOMIALS', Mathematika, 64, pp. 519 - 541, http://dx.doi.org/10.1112/S0025579318000153

Bordellès O; Luca F; Shparlinski IE, 2018, 'On the error term of a lattice counting problem', Journal of Number Theory, 182, pp. 19 - 36, http://dx.doi.org/10.1016/j.jnt.2017.07.019

Shparlinski IE; Zumalacárregui A, 2018, 'Sums of inverses in thin sets of finite fields', Proceedings of the American Mathematical Society, 146, pp. 1377 - 1388, http://dx.doi.org/10.1090/proc/13915

Pomerance C; Shparlinski I, 2018, 'CONNECTED COMPONENTS OF THE GRAPH GENERATED BY POWER MAPS IN PRIME FINITE FIELDS', Integers : Electronic Journal of Combinatorial Number Theory, 18A, pp. 1 - 8, http://math.colgate.edu/~integers/vol18a.html

Shkredov ID; Shparlinski IE, 2018, 'Double Character Sums with Intervals and Arbitrary Sets', Proceedings of the Steklov Institute of Mathematics, 303, pp. 239 - 258

Sha M; Shparlinski IE, 2018, 'Effective results on linear dependence for elliptic curves', Pacific Journal of Mathematics, 295, pp. 123 - 144, http://dx.doi.org/10.2140/pjm.2018.295.123

Shparlinski I; Voloch JF, 2018, 'Generators of Elliptic Curves over Finite Fields', Bulletin of the Institute of Mathematics Academia Sinica, 9, pp. 657 - 670, https://web.ma.utexas.edu/users/voloch/Preprints/EC-Generators.pdf

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2018, 'Multiplicative congruences with variables from short intervals', Journal d'Analyse Mathematique, 124, pp. 117 - 147, http://dx.doi.org/10.1007/s11854-014-0029-2

Macourt S; Shkredov ID; Shparlinski IE, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2

Simon M; Shkredov I; Shparlinski I, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On abelian multiplicatively dependent points on a curve in a torus', The Quarterly Journal of Mathematics, http://dx.doi.org/10.1093/qmath/hax045

Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2018, 'On multiplicatively dependent vectors of algebraic numbers', Transactions of the American Mathematical Society, 370, pp. 6221 - 6244, http://dx.doi.org/10.1090/tran/7115

Heyman R; Shparlinski IE, 2018, 'On shifted Eisenstein polynomials', Periodica Mathematica Hungarica, 69, pp. 170 - 181, http://dx.doi.org/10.1007/s10998-014-0061-0

Shparlinski IE; Sutherland AV, 2018, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, 14, pp. 285 - 297, http://dx.doi.org/10.1007/s10208-013-9181-9

Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Orbits of Polynomial Dynamical Systems Modulo Primes', Proceedings of the American Mathematical Society, 146, pp. 2015 - 2025, http://dx.doi.org/10.1090/proc/13904

D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437

Banks WD; Guo VZ; Shparlinski IE, 2018, 'Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$', Indagationes Mathematicae, 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002

Sha M; Shparlinski IE, 2018, 'The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height', Indagationes Mathematicae, 28, pp. 306 - 320, http://dx.doi.org/10.1016/j.indag.2016.07.004

Dietmann R; Elsholtz C; Shparlinski IE, 2017, 'Prescribing the binary digits of squarefree numbers and quadratic residues', Transactions of the American Mathematical Society, 369, pp. 8369 - 8388, http://dx.doi.org/10.1090/tran/6903

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2017, 'On Functional Graphs of Quadratic Polynomials', Experimental Mathematics, pp. 1 - 9, http://dx.doi.org/10.1080/10586458.2017.1391725

Shparlinski IE; Yau KH, 2017, 'Double exponential sums with exponential functions', International Journal of Number Theory, 13, pp. 2531 - 2543, http://dx.doi.org/10.1142/S179304211750141X

Bell J; Shparlinski IE, 2017, 'Power series approximations to Fekete polynomials', Journal of Approximation Theory, 222, pp. 132 - 142, http://dx.doi.org/10.1016/j.jat.2017.07.002

Banks WD; Shparlinski IE, 2017, 'On coincidences among quadratic fields generated by the shanks sequence', Quarterly Journal of Mathematics, 68, pp. 465 - 484, http://dx.doi.org/10.1093/qmath/haw054

Pomerance C; Shparlinski IE, 2017, 'Connected components of the graph generated by power maps in prime finite fields', , http://arxiv.org/abs/1703.09292v2

Shparlinski IE; Weingartner AJ, 2017, 'An explicit polynomial analogue of Romanoff's theorem', Finite Fields and their Applications, 44, pp. 22 - 33, http://dx.doi.org/10.1016/j.ffa.2016.11.002

Shparlinski IE; Sutherland AV, 2017, 'Finding elliptic curves with a subgroup of prescribed size', International Journal of Number Theory, 13, pp. 133 - 152, http://dx.doi.org/10.1142/S1793042117500099

Shparlinski IE, 2017, 'On the convex hull of the points on multivariate modular hyperbolas', Journal of Number Theory, 171, pp. 71 - 78, http://dx.doi.org/10.1016/j.jnt.2016.07.011

Dubickas A; Sha M; Shparlinski IE, 2017, 'On distances in lattices from algebraic number fields', Moscow Mathematical Journal, 17, pp. 239 - 268, http://dx.doi.org/10.17323/1609-4514-2017-17-2-239-268

Shkredov ID; Shparlinski IE, 2017, 'ON SOME MULTIPLE CHARACTER SUMS', Mathematika, 63, pp. 553 - 560, http://dx.doi.org/10.1112/S0025579317000055

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