Select Publications

Journal articles

Shparlinski IE; Voloch JF, 2021, 'Corrections to “Value sets of sparse polynomials”', Canadian Mathematical Bulletin, pp. 1 - 3, http://dx.doi.org/10.4153/s0008439521000928

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

Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv der Mathematik, vol. 117, pp. 261 - 266, http://dx.doi.org/10.1007/s00013-021-01623-y

Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2

Baker RC; Chen C; Shparlinski IE, 2021, 'Large Weyl sums and Hausdorff dimension', , http://arxiv.org/abs/2108.10439v1

Shkredov ID; Shparlinski IE; Zaharescu A, 2021, 'Bilinear Forms With Modular Square Roots and Twisted Second Moments of Half Integral Weight Dirichlet Series', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnab220

Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, vol. 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5

Baker RC; Chen C; Shparlinski IE, 2021, 'Bounds on the Norms of Maximal Operators on Weyl Sums', , http://arxiv.org/abs/2107.13674v1

Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, vol. 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, vol. 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, vol. 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, vol. 8, http://dx.doi.org/10.1007/s40687-021-00249-4

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'On sparsity of representations of polynomials as linear combinations of exponential functions', , http://arxiv.org/abs/2102.01949v1

Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, vol. 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, vol. 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, http://dx.doi.org/10.1017/S0004972721000083

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

Banks W; Shparlinski I, 2021, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, http://dx.doi.org/10.1112/blms.12524

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, vol. 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478

Ostafe A; Shparlinski IE, 2021, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, pp. 1 - 20, http://dx.doi.org/10.4153/S0008414X21000080

Ghioca D; Shparlinski IE, 2021, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, http://dx.doi.org/10.1016/j.jnt.2021.06.006

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, vol. 27, pp. 903 - 917, http://gateway.webofknowledge.com/gateway/Gateway.cgi?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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 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 IE, 2020, 'An effective local--global principle for algebraic varieties and the sum product problem in finite fields', , http://arxiv.org/abs/2005.02923v1

Banks W; Shparlinski I, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, vol. 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, vol. 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, vol. 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, vol. 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, vol. 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928


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