By Professor Igor Shparlinski

Journal articles

Shparlinski IE, 2012, 'On the distribution of solutions to polynomial congruences', Archiv der Mathematik, 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5

Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2

González JJA; Luca F; Pomerance C; Shparlinski IE, 2012, 'On numbers n dividing the nth term of a linear recurrence', Proceedings of the Edinburgh Mathematical Society, 55, pp. 271 - 289, http://dx.doi.org/10.1017/S0013091510001355

Shparlinski I, 2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ ^-1 in finite fields', Bulletin of the Australian Mathematical Society, 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887

Mans B; Shparlinski IE, 2012, 'Random walks and bisections in random circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7256 LNCS, pp. 542 - 555, http://dx.doi.org/10.1007/978-3-642-29344-3_46

Bourgain J; Konyagin SV; Shparlinski IE, 2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, 2012, pp. 1968 - 2009, http://dx.doi.org/10.1093/imrn/rnr097

Cojocaru AC; Luca F; Shparlinski IE, 2012, 'Erratum: Pseudoprime reductions of elliptic curves (Mathematical Proceedings of the Cambridge Philosophical Society (2009) 146 (513-522))', Mathematical Proceedings of the Cambridge Philosophical Society, 152, pp. 571, http://dx.doi.org/10.1017/S0305004111000399

Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X

Ling S; Shparlinski IE; Steinfeld R; Wang H, 2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, 47, pp. 358 - 367, http://dx.doi.org/10.1016/j.jsc.2011.09.002

Shparlinski IE, 2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, 140, pp. 1199 - 1206, http://dx.doi.org/10.1090/S0002-9939-2011-11203-6

Urroz JJ; Luca F; Shparlinski IE, 2012, 'On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves', Mathematics of Computation, 81, pp. 1093 - 1110, http://dx.doi.org/10.1090/S0025-5718-2011-02543-3

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2012, 'Exponential and character sums with mersenne numbers', Journal of the Australian Mathematical Society, 92, pp. 1 - 13, http://dx.doi.org/10.1017/S1446788712000109

Farashahi RR; Shparlinski IE, 2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, 58, pp. 1242 - 1247, http://dx.doi.org/10.1109/TIT.2011.2170054

Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426

Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719

Cilleruelo J; Shparlinski IE; Zumalacárregui A, 2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, 19, pp. 335 - 343, http://dx.doi.org/10.4310/MRL.2012.v19.n2.a6

Farashahi RR; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, 21, pp. 1 - 10, http://dx.doi.org/10.1080/10586458.2012.632754

Banks WD; Pappalardi F; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, 21, pp. 11 - 25, http://dx.doi.org/10.1080/10586458.2011.606075

Konyagin SV; Shparlinski IE, 2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, 58, pp. 11 - 20, http://dx.doi.org/10.1112/S0025579311002117

Shparlinski IE, 2012, 'On the convex hull of solutions to polynomial congruences', Journal of Number Theory, 132, pp. 254 - 257, http://dx.doi.org/10.1016/j.jnt.2011.06.016

Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010

Shparlinski IE, 2012, 'On the restricted divisor function in arithmetic progressions', Revista Matematica Iberoamericana, 28, pp. 231 - 238, http://dx.doi.org/10.4171/rmi/675

Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, 12, http://dx.doi.org/10.1515/integers-2012-0012

Shparlinski IE, 2011, 'Character sums with fermat quotients', Quarterly Journal of Mathematics, 62, pp. 1031 - 1043, http://dx.doi.org/10.1093/qmath/haq028

Shparlinski IE, 2011, 'Fermat quotients: Exponential sums, value set and primitive roots', Bulletin of the London Mathematical Society, 43, pp. 1228 - 1238, http://dx.doi.org/10.1112/blms/bdr058

Shparlinski IE, 2011, 'On the distribution of irreducible trinomials', Canadian Mathematical Bulletin, 54, pp. 748 - 756, http://dx.doi.org/10.4153/CMB-2011-053-0

Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, 139, pp. 3815 - 3820, http://dx.doi.org/10.1090/S0002-9939-2011-10843-8

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

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

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', , http://arxiv.org/abs/1102.1053v1

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

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

Konyagin SV; Shparlinski IE, 2010, 'On the Convex Hull of the Points on Modular Hyperbolas', , http://arxiv.org/abs/1012.1444v2

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

Back to profile page