By Professor Igor Shparlinski

Journal articles

Broughan KA; Luca F; Shparlinski IE, 2010, 'Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem', Integers, 10, http://dx.doi.org/10.1515/integ.2010.041

Chan TH; Shparlinski IE, 2010, 'Visible Points on Modular Exponential Curves', Bulletin of the Polish Academy of Sciences Mathematics, 58, pp. 17 - 22, http://dx.doi.org/10.4064/ba58-1-2

Фридландер ДБ; Friedlander JB; Гонг K; Gong K; Шпарлинский ИЕ; Shparlinski IE, 2010, 'Суммы значений характеров на сдвинутых простых числах', Математические заметки, 88, pp. 605 - 619, http://dx.doi.org/10.4213/mzm8692

Balasuriya S; Winterhof A; Shparlinski IE, 2009, 'An average bound for character sums with some counter-dependent recurrence sequences', Rocky Mountain Journal of Mathematics, 39, pp. 1403 - 1409, http://dx.doi.org/10.1216/RMJ-2009-39-5-1403

Bourgain J; Konyagin SV; Shparlinski IE, 2009, 'Erratum: Product sets of rationals, multiplicative translates of subgroups in residue rings and fixed points of the discrete logarithm (International Mathematics Research Notices)', International Mathematics Research Notices, 2009, pp. 3146 - 3147, http://dx.doi.org/10.1093/imrn/rnp041

Banks WD; Shparlinski IE, 2009, 'Multiplicative character sums with twice-differentiable functions', Quarterly Journal of Mathematics, 60, pp. 401 - 411, http://dx.doi.org/10.1093/qmath/han023

Katz NM; Shparlinski IE; Xiong M, 2009, 'On character sums with distances on the upper half plane over a finite field', Finite Fields and their Applications, 15, pp. 738 - 747, http://dx.doi.org/10.1016/j.ffa.2009.08.002

Farashahi RR; Shparlinski IE; Voloch JF, 2009, 'On hashing into elliptic curves', Journal of Mathematical Cryptology, 3, pp. 353 - 360, http://dx.doi.org/10.1515/JMC.2009.022

Shparlinski IE, 2009, 'On the distribution of arguments of gauss sums', Kodai Mathematical Journal, 32, pp. 172 - 177, http://dx.doi.org/10.2996/kmj/1238594554

Shparlinski IE, 2009, 'On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture', SIAM Journal on Discrete Mathematics, 23, pp. 2093 - 2099, http://dx.doi.org/10.1137/090770746

Bourgain J; Konyagin SV; Pomerance C; Shparlinski IE, 2009, 'On the smallest pseudopower', Acta Arithmetica, 140, pp. 43 - 55, http://dx.doi.org/10.4064/aa140-1-3

Luca F; Shparlinski IE, 2009, 'On quadratic fields generated by the Shanks sequence', Proceedings of the Edinburgh Mathematical Society, 52, pp. 719 - 729, http://dx.doi.org/10.1017/S001309150700123X

Friedlander JB; Shparlinski IE, 2009, 'Elliptic twin prime conjecture', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 5557 LNCS, pp. 77 - 81, http://dx.doi.org/10.1007/978-3-642-01877-0_8

Shparlinski IE, 2009, 'On a generalisation of a Lehmer problem', Mathematische Zeitschrift, 263, pp. 619 - 631, http://dx.doi.org/10.1007/s00209-008-0434-2

Friedlander JB; Shparlinski IE, 2009, 'On the density of some special primes', Journal of Mathematical Cryptology, 3, pp. 265 - 271, http://dx.doi.org/10.1515/JMC.2009.016

Von Zur Gathen J; Shparlinski IE, 2009, 'Subset sum pseudorandom numbers: Fast generation and distribution', Journal of Mathematical Cryptology, 3, pp. 149 - 163, http://dx.doi.org/10.1515/JMC.2009.007

Shparlinski IE, 2009, 'Bilinear sums with exponential functions', Proceedings of the American Mathematical Society, 137, pp. 2217 - 2224, http://dx.doi.org/10.1090/S0002-9939-09-09882-7

Shparlinski IE, 2009, 'On the values of Kloosterman sums', IEEE Transactions on Information Theory, 55, pp. 2599 - 2601, http://dx.doi.org/10.1109/TIT.2009.2018320

Cojocaru AC; Shparlinski IE, 2009, 'On the embedding degree of reductions of an elliptic curve', Information Processing Letters, 109, pp. 652 - 654, http://dx.doi.org/10.1016/j.ipl.2009.02.018

Balasuriya S; Shparlinski IE; Sutantyo D, 2009, 'Multiplicative character sums with the Euler function', Studia Scientiarum Mathematicarum Hungarica, 46, pp. 223 - 229, http://dx.doi.org/10.1556/SScMath.46.2009.2.1087

Ford K; Luca F; Shparlinski IE, 2009, 'On the largest prime factor of the mersenne numbers', Bulletin of the Australian Mathematical Society, 79, pp. 455 - 463, http://dx.doi.org/10.1017/S0004972709000033

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2009, 'Uniform Distribution of Fractional Parts Related to Pseudoprimes', Canadian Journal of Mathematics, 61, pp. 481 - 502, http://dx.doi.org/10.4153/CJM-2009-025-2

Cojocaru AC; Luca F; Shparlinski IE, 2009, 'Pseudoprime reductions of elliptic curves', Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 513 - 522, http://dx.doi.org/10.1017/S0305004108001758

Shparlinski IE, 2009, 'On some weighted average values of l-functions', Bulletin of the Australian Mathematical Society, 79, pp. 183 - 186, http://dx.doi.org/10.1017/S0004972708001020

Igor S, 2009, 'Some special character sums over elliptic curves', Boletin De La Sociedad Matematica Mexicana, 15, pp. 37 - 40

Abercrombie AG; Banks WD; Shparlinski IE, 2009, 'Arithmetic functions on Beatty sequences', Acta Arithmetica, 136, pp. 81 - 89, http://dx.doi.org/10.4064/aa136-1-6

Shparlinski IE, 2009, 'EXPONENTS OF MODULAR REDUCTIONS OF FAMILIES OF ELLIPTIC CURVES', REVISTA DE LA UNION MATEMATICA ARGENTINA, 50, pp. 69 - 74, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000268682800008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Ahmadi O; Alon N; Blake IF; Shparlinski IE, 2009, 'Graphs with integral spectrum', Linear Algebra and Its Applications, 430, pp. 547 - 552, http://dx.doi.org/10.1016/j.laa.2008.08.020

Pomerance C; Shparlinski IE, 2009, 'On Pseudosquares and Pseudopowers', COMBINATORIAL NUMBER THEORY, pp. 171 - +, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000269082400013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2009, 'On the distribution of solutions to linear equations', Glasnik Matematicki, 44, pp. 7 - 10, http://dx.doi.org/10.3336/gm.44.1.02

Banks WD; Shparlinski IE, 2009, 'Prime numbers with beatty sequences', Colloquium Mathematicum, 115, pp. 147 - 157, http://dx.doi.org/10.4064/cm115-2-1

Banks WD; Shparlinski IE, 2009, 'Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height', Israel Journal of Mathematics, 173, pp. 253 - 277, http://dx.doi.org/10.1007/s11856-009-0091-0

Shparlinski IE, 2009, 'Exponential Sums with Farey Fractions', Bulletin of the Polish Academy of Sciences Mathematics, 57, pp. 101 - 107, http://dx.doi.org/10.4064/ba57-2-2

Shparlinski IE, 2008, 'Arithmetic and geometric progressions in product sets over finite fields', Bulletin of the Australian Mathematical Society, 78, pp. 357 - 364, http://dx.doi.org/10.1017/S0004972708000695

Balasuriya S; Banks WD; Shparlinski IE, 2008, 'Congruences and exponential sums with the sum of aliquot divisors function', International Journal of Number Theory, 4, pp. 903 - 909, http://dx.doi.org/10.1142/S179304210800178X

Shparlinski I, 2008, 'On the size of the Jacobians of curves over finite fields', Bulletin of the Brazilian Mathematical Society, 39, pp. 587 - 595, http://dx.doi.org/10.1007/s00574-008-0006-4

Bourgain J; Konyagin SV; Shparlinski IE, 2008, 'Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm', International Mathematics Research Notices, 2008, http://dx.doi.org/10.1093/imrn/rnn090

Ford K; Shparlinski I, 2008, 'On curves over finite fields with Jacobians of small exponent', International Journal of Number Theory, 4, pp. 819 - 826, http://dx.doi.org/10.1142/S1793042108001687

Luca F; Shparlinski IE, 2008, 'On quadratic fields generated by polynomials', Archiv Der Mathematik, 91, pp. 399 - 408, http://dx.doi.org/10.1007/s00013-008-2656-2

Graham SW; Shparlinski IE, 2008, 'On RSA moduli with almost half of the bits prescribed', Discrete Applied Mathematics, 156, pp. 3150 - 3154, http://dx.doi.org/10.1016/j.dam.2007.12.012

Shparlinski IE; Voloch JF, 2008, 'Average distribution of prime ideals in families of number fields', Bulletin of the Brazilian Mathematical Society, 39, pp. 417 - 425, http://dx.doi.org/10.1007/s00574-008-0014-4

Shparlinski IE, 2008, 'Exponential sums and prime divisors of sparse integers', Periodica Mathematica Hungarica, 57, pp. 93 - 99, http://dx.doi.org/10.1007/s10998-008-7093-3

Shparlinski IE, 2008, 'On the solvability of bilinear equations in finite fields', Glasgow Mathematical Journal, 50, pp. 523 - 529, http://dx.doi.org/10.1017/S0017089508004382

Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'PRODUCTS IN RESIDUE CLASSES', MATHEMATICAL RESEARCH LETTERS, 15, pp. 1133 - 1147, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000262382600023&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE; Winterhof A, 2008, 'Visible points on multidimensional modular hyperbolas', Journal of Number Theory, 128, pp. 2695 - 2703, http://dx.doi.org/10.1016/j.jnt.2008.02.011

Shparlinski IE, 2008, 'Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average', Michigan Mathematical Journal, 56, pp. 99 - 111, http://dx.doi.org/10.1307/mmj/1213972400

Kohnen W; Lau YK; Shparlinski IE, 2008, 'On the number of sign changes of hecke eigenvalues of newforms', Journal of the Australian Mathematical Society, 85, pp. 87 - 94, http://dx.doi.org/10.1017/S1446788708000323

Shparlinski I, 2008, 'On the elliptic curve analogue of the sum-product problem', Finite Fields and their Applications, 14, pp. 721 - 726, http://dx.doi.org/10.1016/j.ffa.2007.12.002

Cojocaru AC; Shparlinski IE, 2008, 'Distribution of farey fractions in residue classes and lang-trotter conjectures on average', Proceedings of the American Mathematical Society, 136, pp. 1977 - 1986, http://dx.doi.org/10.1090/S0002-9939-08-09324-6

Shparlinski I, 2008, 'On the exponential sum-product problem', Indagationes Mathematicae, 19, pp. 325 - 331, http://dx.doi.org/10.1016/S0019-3577(08)80006-7

Back to profile page