By Professor Igor Shparlinski

Journal articles

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

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

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

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', 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

Luca F; Sha M; Shparlinski IE, 2017, 'On two functions arising in the study of the euler and carmichael quotients', Colloquium Mathematicum, 149, pp. 179 - 192, http://dx.doi.org/10.4064/cm6910-3-2017

Liu K; Shparlinski IE; Zhang T, 2017, 'Squares in Piatetski-Shapiro sequences', Acta Arithmetica, 181, pp. 239 - 252, http://dx.doi.org/10.4064/aa8644-8-2017

Shparlinski IE, 2016, 'On the additive energy of the distance set in finite fields', Finite Fields and their Applications, 42, pp. 187 - 199, http://dx.doi.org/10.1016/j.ffa.2016.08.001

Shparlinski IE; Yau KH, 2016, 'Bounds of double multiplicative character sums and gaps between residues of exponential functions', Journal of Number Theory, 167, pp. 304 - 316, http://dx.doi.org/10.1016/j.jnt.2016.03.022

Banks WD; Shparlinski IE, 2016, 'Fractional parts of Dedekind sums', International Journal of Number Theory, 12, pp. 1137 - 1147, http://dx.doi.org/10.1142/S179304211650069X

Shparlinski IE, 2016, 'Ratios of Small Integers in Multiplicative Subgroups of Residue Rings', Experimental Mathematics, 25, pp. 273 - 280, http://dx.doi.org/10.1080/10586458.2015.1091754

Shparlinski IE, 2016, 'Linear congruences with ratios', Proceedings of the American Mathematical Society, 144, pp. 2837 - 2846, http://dx.doi.org/10.1090/proc/12949

Shparlinski IE, 2016, 'On small gaps between the elements of multiplicative subgroups of finite fields', Designs, Codes, and Cryptography, 80, pp. 63 - 71, http://dx.doi.org/10.1007/s10623-015-0063-9

Harman G; Shparlinski IE, 2016, 'Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients', International Mathematics Research Notices, 2016, pp. 1424 - 1446, http://dx.doi.org/10.1093/imrn/rnv182

Camburu OM; Ciolan EA; Luca F; Moree P; Shparlinski IE, 2016, 'Cyclotomic coefficients: Gaps and jumps', Journal of Number Theory, 163, pp. 211 - 237, http://dx.doi.org/10.1016/j.jnt.2015.11.020

Shparlinski IE, 2016, 'SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS', Bulletin of the Australian Mathematical Society, 93, pp. 364 - 371, http://dx.doi.org/10.1017/S0004972715001240

Koh D; Shen CY; Shparlinski I, 2016, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, 26, pp. 1415 - 1441, http://dx.doi.org/10.1007/s12220-015-9595-5

Chang MC; Shparlinski IE, 2016, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, 282, pp. 935 - 954, http://dx.doi.org/10.1007/s00209-015-1571-z

Banks WD; Guo VZ; Shparlinski IE, 2016, 'Almost primes of the form ⌊p^c⌋', Indagationes Mathematicae, 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002

Heyman R; Shparlinski IE, 2016, 'Counting irreducible binomials over finite fields', Finite Fields and their Applications, 38, pp. 1 - 12, http://dx.doi.org/10.1016/j.ffa.2015.12.001

Munsch M; Shparlinski IE, 2016, 'Upper and Lower Bounds for Higher Moments of Theta Functions', Quarterly Journal of Mathematics, 67, pp. 53 - 73, http://dx.doi.org/10.1093/qmath/hav039

Banks WD; Shparlinski IE, 2016, 'On the number of distinct quadratic fields generated by the Shanks sequence', On the number of distinct quadratic fields generated by the Shanks sequence, http://arxiv.org/abs/1602.06473v1

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