By Professor Igor Shparlinski

Journal articles

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', , http://arxiv.org/abs/1602.06473v1

Shparlinski IE, 2016, 'Groups generated by iterations of polynomials over finite fields', Proceedings of the Edinburgh Mathematical Society, 59, pp. 235 - 245, http://dx.doi.org/10.1017/S0013091515000097

Shparlinski IE; Zhang T, 2016, 'Cancellations amongst Kloosterman sums', Acta Arithmetica, 176, pp. 201 - 210, http://dx.doi.org/10.4064/aa8365-6-2016

Nguyen PQ; Shparlinski IE, 2016, 'Counting Co-cyclic lattices', SIAM Journal on Discrete Mathematics, 30, pp. 1358 - 1370, http://dx.doi.org/10.1137/15M103950X

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2016, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, 116, pp. 87 - 122, http://dx.doi.org/10.1016/j.jctb.2015.07.003

Rivat J; Shparlinski IE, 2016, 'Multiples of squares in short intervals', Functiones et Approximatio, Commentarii Mathematici, 54, pp. 57 - 63, http://dx.doi.org/10.7169/facm/2016.54.1.5

Shparlinski IE, 2016, 'On bilinear exponential and character sums with reciprocals of polynomials', Mathematika, 62, pp. 842 - 859, http://dx.doi.org/10.1112/S0025579316000036

Banks WD; Shparlinski IE, 2016, 'On Gauss sums and the evaluation of Stechkin's constant', Mathematics of Computation, 85, pp. 2569 - 2581, http://dx.doi.org/10.1090/mcom3056

Fité F; Shparlinski IE, 2016, 'On the singularity of the demjanenko matrix of quotients of fermat curves', Proceedings of the American Mathematical Society, 144, pp. 55 - 63, http://dx.doi.org/10.1090/proc12717

Shparlinski IE, 2016, 'Polynomial values in small subgroups of finite fields', Revista Matematica Iberoamericana, 32, pp. 1127 - 1136, http://dx.doi.org/10.4171/RMI/909

Bretèche RDL; Sha M; Shparlinski IE; Voloch JF, 2015, 'The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves', Mathematische Zeitschrift, 290, pp. 831 - 855, http://dx.doi.org/10.1007/s00209-018-2042-0

Chang MC; Shparlinski IE, 2015, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, http://dx.doi.org/10.1007/s00209-015-1571-z

Shparlinski IE, 2015, 'Distribution of polynomial discriminants modulo a prime', Archiv der Mathematik, 105, pp. 251 - 259, http://dx.doi.org/10.1007/s00013-015-0806-x

Dubickas A; Sha M; Shparlinski I, 2015, 'Explicit form of Cassels' p-adic Embedding Theorem for Number Fields', Canadian Journal of Mathematics, 67, pp. 1046 - 1064, http://dx.doi.org/10.4153/CJM-2015-021-2

Konyagin SV; Shparlinski IE, 2015, 'Quadratic non-residues in short intervals', Proceedings of the American Mathematical Society, 143, pp. 4261 - 4269, http://dx.doi.org/10.1090/S0002-9939-2015-12584-1

Munsch M; Shparlinski IE, 2015, 'Congruences with intervals and subgroups modulo a prime', Michigan Mathematical Journal, 64, pp. 655 - 672, http://dx.doi.org/10.1307/mmj/1441116662

Heyman R; Shparlinski IE, 2015, 'On the greatest common divisor of shifted sets', Journal of Number Theory, 154, pp. 63 - 73, http://dx.doi.org/10.1016/j.jnt.2015.02.012

Blackburn SR; Konyagin SV; Shparlinski IE, 2015, 'Counting additive decompositions of quadratic residues in finite fields', Functiones et Approximatio, Commentarii Mathematici, 52, pp. 223 - 227, http://dx.doi.org/10.7169/facm/2015.52.2.3

Shparlinski IE, 2015, 'Small discriminants of complex multiplication fields of elliptic curves over finite fields', Czechoslovak Mathematical Journal, 65, pp. 381 - 388, http://dx.doi.org/10.1007/s10587-015-0183-4

Roche-Newton O; Shparlinski IE, 2015, 'Polynomial values in subfields and affine subspaces of finite fields', Quarterly Journal of Mathematics, 66, pp. 693 - 706, http://dx.doi.org/10.1093/qmath/hau032

Shparlinski IE, 2015, 'Close values of shifted modular inversions and the decisional modular inversion hidden number problem', Advances in Mathematics of Communications, 9, pp. 169 - 176, http://dx.doi.org/10.3934/amc.2015.9.169

Shparlinski IE; Sutherland AV, 2015, 'On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average', LMS Journal of Computation and Mathematics, 18, pp. 308 - 322, http://dx.doi.org/10.1112/S1461157015000017

Koh D; Shen CY; Shparlinski I, 2015, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, http://dx.doi.org/10.1007/s12220-015-9595-5

Gómez-Pérez D; Shparlinski IE, 2015, 'Subgroups generated by rational functions in finite fields', Monatshefte fur Mathematik, 176, pp. 241 - 253, http://dx.doi.org/10.1007/s00605-014-0697-0

Shparlinski IE, 2015, 'Cayley graphs generated by small degree polynomials over finite fields', SIAM Journal on Discrete Mathematics, 29, pp. 376 - 381, http://dx.doi.org/10.1137/14095813X

Bourgain J; Konyagin SV; Shparlinski IE, 2015, 'Character sums and deterministic polynomial root finding in finite fields', Mathematics of Computation, 84, pp. 2969 - 2977, http://dx.doi.org/10.1090/mcom/2946

Von Zur Gathen J; Shparlinski IE, 2015, 'Circulant graphs and GCD and LCM of subsets', Information Processing Letters, 115, pp. 134 - 138, http://dx.doi.org/10.1016/j.ipl.2014.07.014

Sha M; Shparlinski IE, 2015, 'Lang-trotter and sato-tate distributions in single and double parametric families of elliptic curves', Acta Arithmetica, 170, pp. 299 - 325, http://dx.doi.org/10.4064/aa170-4-1

Kurlberg P; Luca F; Shparlinski IE, 2015, 'On the fixed points of the map x→x^x modulo a prime', Mathematical Research Letters, 22, pp. 141 - 168, http://dx.doi.org/10.4310/MRL.2015.v22.n1.a8

Shparlinski IE, 2015, 'On the product of small Elkies primes', Proceedings of the American Mathematical Society, 143, pp. 1441 - 1448, http://dx.doi.org/10.1090/S0002-9939-2014-12345-8

Shparlinski I, 2015, 'Points on Varieties over Finite Fields in Small Boxes', Contemporary Mathematics, 655, pp. 209 - 233, http://dx.doi.org/10.1090/conm/655/13235

Chang MC; Shparlinski IE, 2014, 'Double character sums over subgroups and intervals', Bulletin of the Australian Mathematical Society, 90, pp. 376 - 390, http://dx.doi.org/10.1017/S0004972714000227

Chang MC; Cilleruelo J; Garaev MZ; Hernández J; Shparlinski IE; Zumalacárregui A, 2014, 'Points on curves in small boxes and applications', Michigan Mathematical Journal, 63, pp. 503 - 534, http://dx.doi.org/10.1307/mmj/1409932631

Friedlander JB; Shparlinski IE, 2014, 'Enumeration of certain varieties over a finite field', Proceedings of the American Mathematical Society, 142, pp. 2615 - 2623, http://dx.doi.org/10.1090/S0002-9939-2014-11999-X

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