Select Publications

Journal articles

Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, 64, http://dx.doi.org/10.1016/j.jco.2020.101542

Shparlinski IE; Thuswaldner JM, 2021, 'Weyl sums over integers with digital restrictions', , http://arxiv.org/abs/2105.04835v1

Baker RC; Munsch M; Shparlinski IE, 2021, 'Additive energy and a large sieve inequality for sparse sequences', , http://arxiv.org/abs/2103.12659v2

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, 'Energy bounds for modular roots and their applications', , http://arxiv.org/abs/2103.09405v1

Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743

Sha M; Shparlinski IE, 2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363

Mérai L; Shparlinski IE, 2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, 8, http://dx.doi.org/10.1007/s40687-021-00249-4

Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, 219, pp. 228 - 236, http://dx.doi.org/10.1016/j.jnt.2020.09.020

Shparlinski IE, 2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386

Shparlinski IE; Stewart CL, 2021, 'Counting solvable s-unit equations', Proceedings of the American Mathematical Society, 149, pp. 5119 - 5129, http://dx.doi.org/10.1090/proc/15674

Shparlinski IE; Voloch JF, 2021, 'Erratum: Value sets of sparse polynomials (Canadian Mathematical Bulletin (2020) 63 (187-196) DOI: 10.4153/xxxx)', Canadian Mathematical Bulletin, http://dx.doi.org/10.4153/S0008439521000928

Shparlinski IE; Wang Q, 2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, 35, pp. 976 - 987, http://dx.doi.org/10.1137/20M1357731

Kerr B; Mello J; Shparlinski IE, 2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, 27, pp. 903 - 917, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', New York Journal of Mathematics, 27, pp. 903 - 917

Brandes J; Shparlinski IE, 2020, 'Two-dimensional Weyl sums failing square-root cancellation along lines', , http://arxiv.org/abs/2012.08877v1

Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, http://dx.doi.org/10.1016/j.aim.2020.107369

Shparlinski IE, 2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, 68, http://dx.doi.org/10.1016/j.ffa.2020.101747

Chen C; Kerr B; Maynard J; Shparlinski I, 2020, 'Metric theory of Weyl sums', , http://arxiv.org/abs/2011.09306v1

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, 34, pp. 2124 - 2136, http://dx.doi.org/10.1137/20M1325502

Di Benedetto D; Garaev MZ; Garcia VC; Gonzalez-Sanchez D; Shparlinski IE; Trujillo CA, 2020, 'New estimates for exponential sums over multiplicative subgroups and intervals in prime fields', Journal of Number Theory, 215, pp. 261 - 274, http://dx.doi.org/10.1016/j.jnt.2020.02.004

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, 'On the distribution of modular square roots of primes', , http://arxiv.org/abs/2009.03460v1

Chen C; Shparlinski IE, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, 214, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Chen C; Shparlinski IE, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, http://dx.doi.org/10.1016/j.aim.2020.107216

Liu K; Shparlinski IE; Zhang T, 2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, 293, pp. 1505 - 1514, http://dx.doi.org/10.1002/mana.201900006

Shparlinski IE; Stewart CL, 2020, 'Counting solvable $S$-unit equations', , http://arxiv.org/abs/2007.15170v1

Gómez-Pérez D; Mérai L; Shparlinski IE, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, 71, pp. 637 - 648, http://dx.doi.org/10.1093/qmathj/haz055

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, 'Polynomial Equations in Subgroups and Applications', , http://arxiv.org/abs/2005.05315v1

Kerr B; Mello J; Shparlinski I, 2020, 'An effective local-global principle for algebraic varieties and the sum product problem in finite fields', , http://arxiv.org/abs/2005.02923v3

Banks W; Shparlinski I, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7

Chen C; Kerr B; Shparlinski I, 2020, 'Metric theory of lower bounds on Weyl sums', , http://arxiv.org/abs/2004.02539v3

Chen C; Shparlinski IE, 2020, 'Hybrid bounds on two-parametric family Weyl sums along smooth curves', , http://arxiv.org/abs/2003.02419v1

Shparlinski IE; Voloch JF, 2020, 'Value Sets of Sparse Polynomials', Canadian Mathematical Bulletin, 63, pp. 187 - 196, http://dx.doi.org/10.4153/S0008439519000316

Kerr B; Shparlinski IE, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, 6, http://dx.doi.org/10.1007/s40993-020-0191-9

Mérai L; Shparlinski IE, 2020, 'Unlikely intersections over finite fields: Polynomial orbits in small subgroups', Discrete and Continuous Dynamical Systems- Series A, 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070

Li R; Shparlinski IE, 2020, 'Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers', , http://arxiv.org/abs/2001.09721v1

Kerr B; Mérai L; Shparlinski IE, 2020, 'On digits of Mersenne numbers', , http://arxiv.org/abs/2001.03380v4

Pakovich F; Shparlinski IE, 2020, 'Level curves of rational functions nd unimodular points on rational curves', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Shparlinski IE, 2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, 148, pp. 2371 - 2377, http://dx.doi.org/10.1090/proc/14901

Korolev M; Shparlinski I, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions', Pacific Journal of Mathematics, 304, pp. 505 - 522, http://dx.doi.org/10.2140/pjm.2020.304.505

Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737

Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369

Shparlinski I; Kerr B, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, pp. 1 - 21, http://dx.doi.org/10.1007/s40993-020-0191-9

Shparlinski I; Voloch F, 2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, 21, pp. 931 - 941, http://dx.doi.org/10.2422/2036-2145.201811_007

Shparlinski I; Banks W, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7

Mérai L; Shparlinski IE, 2020, 'Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$', Mathematics of Computation, 322, pp. 911 - 922, http://dx.doi.org/10.1090/mcom/3467

Shparlinski I; Chen C, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Ricotta G; Royer E; Shparlinski I, 2020, 'Kloosterman paths of prime powers moduli, II', Bulletin de la Societe Mathematique de France, 148, pp. 173 - 188, http://dx.doi.org/10.24033/bsmf.2802

Shparlinski IE; Technau M, 2020, 'Kloosterman sums with twice-differentiable functions', Functiones et Approximatio Commentarii Mathematici, 63, pp. 113 - 124, http://dx.doi.org/10.7169/facm/1845


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