By Professor Igor Shparlinski

Journal articles

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', 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

Banks WD; Luca F; Shparlinski IE, 2007, 'Estimates for Wieferich numbers', Ramanujan Journal, 14, pp. 361 - 378, http://dx.doi.org/10.1007/s11139-007-9030-z

Becheanu M; Luca F; Shparlinski IE, 2007, 'On the sums of complementary divisors', INTERNATIONAL JOURNAL OF NUMBER THEORY, 3, pp. 635 - 648, http://dx.doi.org/10.1142/S1793042107001152

Blake IF; Shparlinski IE, 2007, 'Statistical distribution and collisions of VSH', JOURNAL OF MATHEMATICAL CRYPTOLOGY, 1, pp. 329 - 349, http://dx.doi.org/10.1515/JMC.2007.016

Balasuriya S; Shparlinski IE, 2007, 'Character sums with subsequence sums', Periodica Mathematica Hungarica, 55, pp. 215 - 221, http://dx.doi.org/10.1007/s10998-007-4215-4

Ahmadi O; Shparlinski IE, 2007, 'Geometric progressions in sumsets over finite fields', Monatshefte fur Mathematik, 152, pp. 177 - 185, http://dx.doi.org/10.1007/s00605-007-0471-7

Ahmadi O; Shparlinski IE, 2007, 'Distribution of matrices with restricted entries over finite fields', Indagationes Mathematicae, 18, pp. 327 - 337, http://dx.doi.org/10.1016/S0019-3577(07)00013-4

Luca F; Shparlinski IE, 2007, 'PSEUDOPRIMES IN CERTAIN LINEAR RECURRENCES', Albanian Journal of Mathematics, 1, http://dx.doi.org/10.51286/albjm/1189355988

Shparlinski IE; Winterhof A, 2007, 'Quantum period reconstruction of approximate sequences', Information Processing Letters, 103, pp. 211 - 215, http://dx.doi.org/10.1016/j.ipl.2007.02.019

Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', Journal of Number Theory, 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003

Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', JOURNAL OF NUMBER THEORY, 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003

Shparlinski IE, 2007, 'Character sums over shifted smooth numbers', Proceedings of the American Mathematical Society, 135, pp. 2699 - 2705, http://dx.doi.org/10.1090/S0002-9939-07-08785-0

Shparlinski IE, 2007, 'Distribution of roots of polynomial congruences', International Journal of Mathematics and Mathematical Sciences, 2007, http://dx.doi.org/10.1155/2007/37853

Luca F; Shparlinski IE, 2007, 'Arithmetic functions with linear recurrence sequences', Journal of Number Theory, 125, pp. 459 - 472, http://dx.doi.org/10.1016/j.jnt.2006.12.006

Shparlinski IE, 2007, 'Communication complexity of some number theoretic functions', Applied Mathematics Letters, 20, pp. 872 - 875, http://dx.doi.org/10.1016/j.aml.2006.05.024

Luca F; Shparlinski IE, 2007, 'On finite fields for pairing based cryptography', ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 1, pp. 281 - 286, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254707500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

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