By Professor Igor Shparlinski

Journal articles

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

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→xx 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

Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, 'Interpolation and approximation of polynomials in finite fields over a short interval from noisy values', Experimental Mathematics, 23, pp. 241 - 260, http://dx.doi.org/10.1080/10586458.2014.890918

Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9

Shparlinski IE; Sutantyo D, 2014, 'Distribution of elliptic twin primes in isogeny and isomorphism classes', Journal of Number Theory, 137, pp. 1 - 15, http://dx.doi.org/10.1016/j.jnt.2013.10.018

Luca F; Shparlinski IE, 2014, 'On the counting function of elliptic carmichael numbers', Canadian Mathematical Bulletin, 57, pp. 105 - 112, http://dx.doi.org/10.4153/CMB-2012-037-4

Shparlinski IE, 2014, 'On the distribution of points on the generalized markoff-hurwitz and dwork hypersurfaces', International Journal of Number Theory, 10, pp. 151 - 160, http://dx.doi.org/10.1142/S1793042113500863

Chen Z; Shparlinski IE; Winterhof A, 2014, 'Covering sets for limited-magnitude errors', IEEE Transactions on Information Theory, 60, pp. 5315 - 5321, http://dx.doi.org/10.1109/TIT.2014.2338078

Shparlinski IE, 2014, 'Distribution of exponential functions modulo a prime power', Journal of Number Theory, 143, pp. 224 - 231, http://dx.doi.org/10.1016/j.jnt.2014.04.010

Chang MC; Kerr B; Shparlinski IE; Zannier U, 2014, 'Elements of large order on varieties over prime finite fields', Journal De Theorie Des Nombres De Bordeaux, 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880

Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, 547, pp. 117 - 121, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Ahmadi O; Shparlinski IE, 2014, 'Exponential sums over points of elliptic curves', Journal of Number Theory, 140, pp. 299 - 313, http://dx.doi.org/10.1016/j.jnt.2014.01.016

Shparlinski IE, 2014, 'Multiple exponential and character sums with monomials', Mathematika, 60, pp. 363 - 373, http://dx.doi.org/10.1112/S0025579314000084

Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809

Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, 89, pp. 300 - 307, http://dx.doi.org/10.1017/S0004972713000671

Ling S; Shparlinski I; Wang H, 2014, 'On the multidimensional distribution of the Naor-Reingold pseudo-random function', Mathematics of Computation, 83, pp. 2429 - 2434, http://dx.doi.org/10.1090/S0025-5718-2014-02794-4

Shparlinski IE, 2014, 'Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields', Journal of Symbolic Computation, 64, pp. 35 - 41, http://dx.doi.org/10.1016/j.jsc.2013.12.005

Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, 70, pp. 301 - 325

Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv Der Mathematik, 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0

Blake IF; Luca F; Shparlinski IE, 2014, 'VSH and multiplicative modular relations between small primes with polynomial exponents', Applicable Algebra in Engineering, Communications and Computing, 25, pp. 181 - 188, http://dx.doi.org/10.1007/s00200-014-0219-2

Shparlinski IE; Sutherland AV, 2014, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, pp. 1 - 13, http://dx.doi.org/10.1007/s10208-013-9181-9

Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470

Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011

Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022

Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8

Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, 24, pp. 930 - 938, http://dx.doi.org/10.1016/j.indag.2013.02.005

Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte Fur Mathematik, 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x

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