By Professor Igor Shparlinski

Journal articles

Luca F; Shparlinski IE, 2011, 'On the g-Ary expansions of middle binomial coefficients and catalan numbers', Rocky Mountain Journal of Mathematics, 41, pp. 1291 - 1301, http://dx.doi.org/10.1216/RMJ-2011-41-4-1291

Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, 7, pp. 1557 - 1571, http://dx.doi.org/10.1142/S1793042111004484

Balog A; Broughan KA; Shparlinski IE, 2011, 'On the number of solutions of exponential congruences', Acta Arithmetica, 148, pp. 93 - 103, http://dx.doi.org/10.4064/aa148-1-7

Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, 148, pp. 77 - 92, http://dx.doi.org/10.4064/aa148-1-6

Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, 25, pp. 50 - 71, http://dx.doi.org/10.1137/100798466

Shparlinski IE, 2011, 'Bounds of multiplicative character sums with Fermat quotients of primes', Bulletin of the Australian Mathematical Society, 83, pp. 456 - 462, http://dx.doi.org/10.1017/S000497271000198X

Fouvry E; Luca F; Pappalardi F; Shparlinski IE, 2011, 'Counting dihedral and quaternionic extensions', Transactions of the American Mathematical Society, 363, pp. 3233 - 3253, http://dx.doi.org/10.1090/S0002-9947-2011-05233-5

Shparlinski IE, 2011, 'On small solutions to quadratic congruences', Journal of Number Theory, 131, pp. 1105 - 1111, http://dx.doi.org/10.1016/j.jnt.2010.12.002

Shparlinski IE, 2011, 'Exponential sums with consecutive modular roots of an integer', Quarterly Journal of Mathematics, 62, pp. 207 - 213, http://dx.doi.org/10.1093/qmath/hap023

Shparlinski IE, 2011, 'On the average distribution of pseudorandom numbers generated by nonlinear permutations', Mathematics of Computation, 80, pp. 1053 - 1061, http://dx.doi.org/10.1090/S0025-5718-2010-02408-1

Křížek M; Luca F; Shparlinski IE; Somer L, 2011, 'On the complexity of testing elite primes', Journal of Integer Sequences, 14, pp. 1 - 5

Fouvry E; Shparlinski IE, 2011, 'On a ternary quadratic form over primes', Acta Arithmetica, 150, pp. 285 - 314, http://dx.doi.org/10.4064/aa150-3-5

Konyagin SV; Shparlinski IE, 2011, 'On convex hull of points on modular hyperbolas', Moscow Journal of Combinatorics and Number Theory, 1, pp. 43 - 51

Fouvry E; Shparlinski IE, 2011, 'Smooth shifted monomial products', Publicationes Mathematicae Debrecen, 79, pp. 423 - 432, http://dx.doi.org/10.5486/PMD.2011.5089

Bibak K; Shparlinski IE, 2011, 'On Fully Split Lacunary Polynomials in Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, 59, pp. 197 - 202, http://dx.doi.org/10.4064/ba59-3-1

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, abs/1102.1053

Ford K; Khan MR; Shparlinski IE, 2010, 'Geometric properties of points on modular hyperbolas', Proceedings of the American Mathematical Society, 138, pp. 4177 - 4185, http://dx.doi.org/10.1090/S0002-9939-2010-10561-0

Farashahi RR; Shparlinski IE, 2010, 'On pseudopoints of algebraic curves', Archiv Der Mathematik, 95, pp. 529 - 537, http://dx.doi.org/10.1007/s00013-010-0200-7

Luca F; Shparlinski IE, 2010, 'On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers', Annals of Combinatorics, 14, pp. 507 - 524, http://dx.doi.org/10.1007/s00026-011-0074-9

Friedlander JB; Gong K; Shparlinskii IE, 2010, 'Character sums over shifted primes', Mathematical Notes, 88, pp. 585 - 598, http://dx.doi.org/10.1134/S0001434610090312

Gutierrez J; Shparlinski IE, 2010, 'Expansion of orbits of some dynamical systems over finite fields', Bulletin of the Australian Mathematical Society, 82, pp. 232 - 239, http://dx.doi.org/10.1017/S0004972709001270

Karabina K; Menezes A; Pomerance C; Shparlinski IE, 2010, 'On the asymptotic effectiveness of Weil descent attacks', Journal of Mathematical Cryptology, 4, pp. 175 - 191, http://dx.doi.org/10.1515/JMC.2010.007

Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, 16, pp. 320 - 328, http://dx.doi.org/10.1016/j.ffa.2010.05.002

von zur Gathen J; Mignotte M; Shparlinski IE, 2010, 'Approximate polynomial gcd: Small degree and small height perturbations', Journal of Symbolic Computation, 45, pp. 879 - 886, http://dx.doi.org/10.1016/j.jsc.2010.04.001

Bourgain J; Ford K; Konyagin SV; Shparlinski IE, 2010, 'On the divisibility of Fermat quotients', Michigan Mathematical Journal, 59, pp. 313 - 328, http://dx.doi.org/10.1307/mmj/1281531459

Ostafe A; Shparlinski IE; Winterhof A, 2010, 'On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences', Advances in Mathematics of Communications, 4, pp. 369 - 379, http://dx.doi.org/10.3934/amc.2010.4.369

Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, 138, pp. 2653 - 2656, http://dx.doi.org/10.1090/S0002-9939-10-10404-3

Shparlinski IE; Winterhof A, 2010, 'Partitions into two Lehmer numbers', Monatshefte Fur Mathematik, 160, pp. 429 - 441, http://dx.doi.org/10.1007/s00605-009-0130-2

Glebsky L; Shparlinski IE, 2010, 'Short cycles in repeated exponentiation modulo a prime', Designs Codes and Cryptography, 56, pp. 35 - 42, http://dx.doi.org/10.1007/s10623-009-9339-2

Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, 23, pp. 501 - 513, http://dx.doi.org/10.1007/s13163-010-0029-4

Chan TH; Shparlinski IE, 2010, 'On the concentration of points on modular hyperbolas and exponential curves', Acta Arithmetica, 142, pp. 59 - 66, http://dx.doi.org/10.4064/aa142-1-5

Banks WD; Shparlinski IE, 2010, 'Sums with convolutions of Dirichlet characters', Manuscripta Mathematica, 133, pp. 105 - 114, http://dx.doi.org/10.1007/s00229-010-0364-2

Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, 79, pp. 501 - 511, http://dx.doi.org/10.1090/S0025-5718-09-02271-6

Ahmadi O; Shparlinski IE; Voloch JF, 2010, 'Multiplicative order of gauss periods', International Journal of Number Theory, 6, pp. 877 - 882, http://dx.doi.org/10.1142/S1793042110003290

Konyagin SV; Pomerance C; Shparlinski IE, 2010, 'On the distribution of pseudopowers', Canadian Journal of Mathematics, 62, pp. 582 - 594, http://dx.doi.org/10.4153/CJM-2010-020-4

Shparlinski IE, 2010, 'Tate-shafarevich groups and frobenius fields of reductions of elliptic curves', Quarterly Journal of Mathematics, 61, pp. 255 - 263, http://dx.doi.org/10.1093/qmath/hap001

Shparlinski IE, 2010, 'On the size of the Gelfond exponent', Journal of Number Theory, 130, pp. 1056 - 1060, http://dx.doi.org/10.1016/j.jnt.2009.09.005

Iosevich A; Shparlinski IE; Xiong M, 2010, 'Sets with integral distances in finite fields', Transactions of the American Mathematical Society, 362, pp. 2189 - 2204, http://dx.doi.org/10.1090/S0002-9947-09-05004-1

Iosevich A; Shparlinski IE; Xiong M, 2010, 'SETS WITH INTEGRAL DISTANCES IN FINITE FIELDS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362, pp. 2189 - 2204, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000275819200020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2010, 'Numbers at work and play', Notices of the American Mathematical Society, 57, pp. 334 - 342

Ahmadi O; Shparlinski I, 2010, 'Bilinear character sums and sum-product problems on elliptic curves', Proceedings of the Edinburgh Mathematical Society, 53, pp. 1 - 12, http://dx.doi.org/10.1017/S0013091508000771

Shparlinski IE, 2010, 'On point sets in vector spaces over finite fields that determine only acute angle triangles', Bulletin of the Australian Mathematical Society, 81, pp. 114 - 120, http://dx.doi.org/10.1017/S0004972709000719

Shparlinski IE, 2010, 'On quadratic fields generated by discriminants of irreducible trinomials', Proceedings of the American Mathematical Society, 138, pp. 125 - 132, http://dx.doi.org/10.1090/S0002-9939-09-10074-6

Cilleruelo J; Luca F; Quirós A; Shparlinski IE, 2010, 'On squares in polynomial products', Monatshefte Fur Mathematik, 159, pp. 215 - 223, http://dx.doi.org/10.1007/s00605-008-0066-y

Loiperdinger SS; Shparlinski IE, 2010, 'ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS', COLLOQUIUM MATHEMATICUM, 120, pp. 139 - 148, http://dx.doi.org/10.4064/cm120-1-10

Ahmadi O; Shparlinski IE, 2010, 'On the distribution of the number of points on algebraic curves in extensions of finite fields', Mathematical Research Letters, 17, pp. 689 - 699, http://dx.doi.org/10.4310/MRL.2010.v17.n4.a9

Rezaeian Farashahi R; Shparlinski IE, 2010, 'On the number of distinct elliptic curves in some families', Designs Codes and Cryptography, 54, pp. 83 - 99, http://dx.doi.org/10.1007/s10623-009-9310-2

Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0

Pomerance C; Shparlinski IE, 2010, 'Rank statistics for a family of elliptic curves over a function field', Pure and Applied Mathematics Quarterly, 6, pp. 21 - 40, http://dx.doi.org/10.4310/PAMQ.2010.v6.n1.a2

Shparlinski IE, 2010, 'Some counting questions for matrices with restricted entries', Linear Algebra and Its Applications, 432, pp. 155 - 160, http://dx.doi.org/10.1016/j.laa.2009.07.036

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