By Professor Igor Shparlinski

Journal articles

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

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

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

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

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

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

, 2020, 'Correction: Value sets of sparse polynomials (Canadian Mathematical Bulletin (2020) 63 (187-196) DOI: 10.4153/xxxx)', Canadian Mathematical Bulletin, 65, pp. 1071 - 1073, http://dx.doi.org/10.4153/S0008439521000928

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

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

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; 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, 6, pp. 1 - 21, http://dx.doi.org/10.1007/s40993-020-0191-9

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

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

Shparlinski I; Chen C, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, pp. 1 - 48, http://dx.doi.org/10.1016/j.aim.2020.107216

Munsch M; Shparlinski IE, 2020, 'On smooth square-free numbers in arithmetic progressions', Journal of the London Mathematical Society, 101, pp. 1941 - 1067, http://dx.doi.org/10.1112/jlms.12297

Shparlinski I; Gomez-Perez D; Merai L, 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

Munsch M; Shparlinski IE; Yau KH, 2020, 'SMOOTH SQUAREFREE AND SQUAREFULL INTEGERS IN ARITHMETIC PROGRESSIONS', Mathematika, 66, pp. 56 - 70, http://dx.doi.org/10.1112/mtk.12012

Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., 304, pp. 505 - 18, http://dx.doi.org/10.2140/pjm.2020.304.505

Shparlinski I; Banks W, 2020, 'Sums with the Mobius function twisted by characters with powerful moduli', Trans. Amer. Math. Soc., pp. 249 - 272, http://dx.doi.org/10.1090/tran/7914

Shparlinski I, 2020, 'Unlikely intersections over finite fields: polynomial orbits in small subgroups', DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS., Ser.A, 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070

Macourt S; Shparlinski IE, 2019, 'Double sums of Kloosterman sums in finite fields', Finite Fields and their Applications, 60, http://dx.doi.org/10.1016/j.ffa.2019.101575

Shparlinski IE, 2019, 'Bounds on average values of double incomplete Kloosterman sums', Journal of Number Theory, 203, pp. 1 - 11, http://dx.doi.org/10.1016/j.jnt.2019.03.009

Banks WD; Shparlinski IE, 2019, 'Bounds on short character sums and L-functions with characters to a powerful modulus', Journal D Analyse Mathematique, 139, pp. 239 - 263, http://dx.doi.org/10.1007/s11854-019-0060-4

Bordellès O; Dai L; Heyman R; Pan H; Shparlinski IE, 2019, 'On a sum involving the Euler function', Journal of Number Theory, 202, pp. 278 - 297, http://dx.doi.org/10.1016/j.jnt.2019.01.006

Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2019, 'Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz091

Shparlinski IE, 2019, 'ON SHORT PRODUCTS OF PRIMES IN ARITHMETIC PROGRESSIONS', Proceedings of the American Mathematical Society, pp. 977 - 986, http://dx.doi.org/10.1090/proc/14289

Mérai L; Shparlinski IE, 2019, 'Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields', Acta Arithmetica, 188, pp. 401 - 411, http://dx.doi.org/10.4064/aa180307-20-8

Roche-Newton O; Shparlinski IE; Winterhof A, 2019, 'Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions', Annals of Combinatorics, http://dx.doi.org/10.1007/s00026-019-00420-3

Shparlinski I; Zannier U, 2019, 'Arithmetic properties of quadratic exponential polynomials', New York Journal of Mathematics, 25, pp. 207 - 218, https://www.emis.de/journals/NYJM/nyjm/j/2019/25-12p.pdf

Shparlinski IE, 2019, 'Bilinear Forms with Kloosterman and Gauss Sums', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, http://dx.doi.org/10.1090/tran/7506

Shparlinski IE; Voloch JF, 2019, 'Binomial exponential sums', ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE, pp. 1 - 1, http://dx.doi.org/10.2422/2036-2145.201811_007

Petridis G; Shparlinski IE, 2019, 'Bounds on trilinear and quadrilinear exponential sums', Journal d'Analyse Mathématique

Liu K; Shparlinski IE; Zhang T, 2019, 'CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS', Mathematika, 65, pp. 475 - 487, http://dx.doi.org/10.1112/s0025579318000554

Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2019, 'Counting integers with a smooth totient', The Quarterly Journal of Mathematics, pp. 1371 - 1386, http://dx.doi.org/10.1093/qmathj/haz026

El Abdalaoui EH; Shparlinski IE, 2019, 'Disjointness of the Möbius Transformation and Möbius Function', Research in the Mathematical Sciences, 6, http://dx.doi.org/10.1007/s40687-019-0180-6

Breuer F; Shparlinski IE, 2019, 'Lower bounds for periods of Ducci sequences', Bull. Aust. Math. Soc., http://dx.doi.org/10.1017/S0004972719001187

Chen C; Shparlinski IE, 2019, 'New bounds of Weyl sums', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz293

SHPARLINSKI IGORE, 2019, 'ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES', Bulletin of the Australian Mathematical Society, pp. 1 - 4, http://dx.doi.org/10.1017/s0004972718001302

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

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