By Professor Igor Shparlinski

Journal articles

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

Naccache D; Shparlinski IE, 2008, 'Divisibility, Smoothness and Cryptographic Applications', , http://arxiv.org/abs/0810.2067v3

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

Von Zur Gathen J; Shparlinski IE, 2008, 'Approximate polynomial gcd: Small degree and small height perturbations', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4957 LNCS, pp. 276 - 283, http://dx.doi.org/10.1007/978-3-540-78773-0_24

Shparlinski IE, 2008, 'Pseudorandom graphs from elliptic curves', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4957 LNCS, pp. 284 - 292, http://dx.doi.org/10.1007/978-3-540-78773-0_25

Shparlinski IE; Winterhof A, 2008, 'On the number of distances between the coordinates of points on modular hyperbolas', Journal of Number Theory, 128, pp. 1224 - 1230, http://dx.doi.org/10.1016/j.jnt.2007.04.016

Luca F; Shparlinski IE, 2008, 'On the values of the divisor function', Monatshefte fur Mathematik, 154, pp. 59 - 69, http://dx.doi.org/10.1007/s00605-007-0511-3

Blackburn SR; Shparlinski IE, 2008, 'On the average energy of circulant graphs', Linear Algebra and Its Applications, 428, pp. 1956 - 1963, http://dx.doi.org/10.1016/j.laa.2007.11.003

Shparlinski IE, 2008, 'Approximation by several rationals', Bulletin of the Australian Mathematical Society, 77, pp. 325 - 329, http://dx.doi.org/10.1017/S0004972708000373

Shparlinski IE, 2008, 'On a Generalised Lehmer Problem for Arbitrary Powers', , http://arxiv.org/abs/0803.3487v2

Luca F; Shparlinski IE; Thangadurai R, 2008, 'Quadratic non-residues versus primitive roots modulo p', Journal of the Ramanujan Mathematical Society, 23, pp. 97 - 104

Shparlinski IE, 2008, 'On the distribution of kloosterman sums', Proceedings of the American Mathematical Society, 136, pp. 419 - 425, http://dx.doi.org/10.1090/S0002-9939-07-08943-5

Luca F; Shparlinski IE, 2008, 'Arithmetic properties of Apéry numbers', Journal of the London Mathematical Society, 78, pp. 545 - 562, http://dx.doi.org/10.1112/jlms/jdn031

Shparlinski I, 2008, 'Bilinear character sums over elliptic curves', Finite Fields and their Applications, 14, pp. 132 - 141, http://dx.doi.org/10.1016/j.ffa.2006.12.005

Van Dam W; Shparlinski IE, 2008, 'Classical and quantum algorithms for exponential congruences', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5106 LNCS, pp. 1 - 10, http://dx.doi.org/10.1007/978-3-540-89304-2_1

Banks WD; Garaev MZ; Heath-Brown DR; Shparlinski IE, 2008, 'Density of non-residues in Burgess-type intervals and applications', Bulletin of the London Mathematical Society, 40, pp. 88 - 96, http://dx.doi.org/10.1112/blms/bdm111

Bourgain J; Shparlinski IE, 2008, 'Distribution of consecutive modular roots of an integer', Acta Arithmetica, 134, pp. 83 - 91, http://dx.doi.org/10.4064/aa134-1-6

Friedlander JB; Shparlinski IE, 2008, 'Erratum: Least totient in a residue class (Bulletin of the London Mathematical Society (2007) 39 (425-432))', Bulletin of the London Mathematical Society, 40, pp. 532, http://dx.doi.org/10.1112/blms/bdn037

Shparlinski IE, 2008, 'Infinite hilbert class field towers over cyclotomic fields', Glasgow Mathematical Journal, 50, pp. 27 - 32, http://dx.doi.org/10.1017/S0017089507003977

Khan MR; Shparlinski IE; Yankov CL, 2008, 'On the convex closure of the graph of modular inversions', Experimental Mathematics, 17, pp. 91 - 104, http://dx.doi.org/10.1080/10586458.2008.10129021

Shparlinski IE, 2008, 'On the distribution of Kloosterman sums', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136, pp. 419 - 425, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000251536800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'Products in residue classes', Mathematical Research Letters, 15, pp. 1133 - 1147, http://dx.doi.org/10.4310/mrl.2008.v15.n6.a6

Shparlinski IE, 2008, 'On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas', Bulletin of the Polish Academy of Sciences Mathematics, 56, pp. 1 - 7, http://dx.doi.org/10.4064/ba56-1-1

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