By Professor Igor Shparlinski

Journal articles

Shparlinski IE, 2006, 'Primitive Points on a Modular Hyperbola', Bulletin of the Polish Academy of Sciences Mathematics, 54, pp. 193 - 200, http://dx.doi.org/10.4064/ba54-3-1

Shparlinski IE; Winterhof A, 2005, 'On the linear complexity of bounded integer sequences over different moduli', Information Processing Letters, 96, pp. 175 - 177, http://dx.doi.org/10.1016/j.ipl.2005.08.004

Banks WD; Harman G; Shparlinski IE, 2005, 'Distributional properties of the largest prime factor', Michigan Mathematical Journal, 53, pp. 665 - 681, http://dx.doi.org/10.1307/mmj/1133894172

Shparlinski I; Winterhof A, 2005, 'Noisy interpolation of sparse polynomials in finite fields', Applicable Algebra in Engineering Communications and Computing, 16, pp. 307 - 317, http://dx.doi.org/10.1007/s00200-005-0180-1

Ford K; Khan MR; Shparlinski IE; Yankov CL, 2005, 'On the maximal difference between an element and its inverse in residue rings', Proceedings of the American Mathematical Society, 133, pp. 3463 - 3468, http://dx.doi.org/10.1090/S0002-9939-05-07962-1

Shparlinski IE, 2005, 'On the value set of the Ramanujan function', Archiv Der Mathematik, 85, pp. 508 - 513, http://dx.doi.org/10.1007/s00013-005-1322-1

Levieil E; Luca F; Shparlinski IE, 2005, 'Prime divisors of some shifted products', International Journal of Mathematics and Mathematical Sciences, 2005, pp. 3057 - 3073, http://dx.doi.org/10.1155/IJMMS.2005.3057

Banks WD; Shparlinski IE, 2005, 'Prime divisors of palindromes', Periodica Mathematica Hungarica, 51, pp. 1 - 10, http://dx.doi.org/10.1007/s10998-005-0016-6

Shparlinski I; Winterhof A, 2005, 'A hidden number problem in small subgroups', Mathematics of Computation, 74, pp. 2073 - 2080, http://dx.doi.org/10.1090/S0025-5718-05-01797-7

Levieil E; Luca F; Shparlinski IE, 2005, 'Bounding the number of solutions of some congruences', Boletin De La Sociedad Matematica Mexicana, 11, pp. 175 - 180

von zur Gathen J; Shparlinski IE; Stichtenoth H, 2005, 'Finite Fields: Theory and Applications', Oberwolfach Reports, 1, pp. 2913 - 2970, http://dx.doi.org/10.4171/owr/2004/54

Banks WD; Luca F; Saidak F; Shparlinski IE, 2005, 'Values of arithmetical functions equal to a sum of two squares', Quarterly Journal of Mathematics, 56, pp. 123 - 139, http://dx.doi.org/10.1093/qmath/hah039

Garaev MZ; Shparlinski IE, 2005, 'The large sieve inequality with exponential functions and the distribution of mersenne numbers modulo primes', International Mathematics Research Notices, pp. 2391 - 2403, http://dx.doi.org/10.1155/imrn.2005.2391

Banks WD; Luca F; Shparlinski IE, 2005, 'Some divisibility properties of the Euler function', Glasgow Mathematical Journal, 47, pp. 517 - 528, http://dx.doi.org/10.1017/S0017089505002752

Banks WD; Ford K; Luca F; Pappalardi F; Shparlinski IE, 2005, 'Values of the Euler function in various sequences', Monatshefte Fur Mathematik, 146, pp. 1 - 19, http://dx.doi.org/10.1007/s00605-005-0302-7

Klappenecker A; Rötteler M; Shparlinski IE; Winterhof A, 2005, 'On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states', Journal of Mathematical Physics, 46, http://dx.doi.org/10.1063/1.1998831

Cohen SD; Dewar M; Friedlander JB; Panario D; Shparlinski IE, 2005, 'Polynomial gauss sums', Proceedings of the American Mathematical Society, 133, pp. 2225 - 2231, http://dx.doi.org/10.1090/S0002-9939-05-08004-4

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2005, 'Predicting nonlinear pseudorandom number generators', Mathematics of Computation, 74, pp. 1471 - 1494, http://dx.doi.org/10.1090/S0025-5718-04-01698-9

Banks WD; Luca F; Shparlinski IE, 2005, 'Irrationality of power series for various number theoretic functions', Manuscripta Mathematica, 117, pp. 183 - 197, http://dx.doi.org/10.1007/s00229-005-0564-3

Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over Fp and residue races', Journal of Number Theory, 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

Luca F; Shparlinski IE, 2005, 'On the exponent of the group of points on elliptic curves in extension fields', International Mathematics Research Notices, pp. 1391 - 1409, http://dx.doi.org/10.1155/imrn.2005.1391

Shparlinski I, 2005, 'Book Review: Report on global methods for combinatorial isoperimetric problems', Mathematics of Computation, 74, pp. 1033 - 1052, http://dx.doi.org/10.1090/s0025-5718-04-01757-0

Hess F; Shparlinski IE, 2005, 'On the linear complexity and multidimensional distribution of congruential generators over elliptic curves', Designs Codes and Cryptography, 35, pp. 111 - 117, http://dx.doi.org/10.1007/s10623-003-6153-0

Shparlinski IE, 2005, 'On the singularity of generalised Vandermonde matrices over finite fields', Finite Fields and their Applications, 11, pp. 193 - 199, http://dx.doi.org/10.1016/j.ffa.2004.11.001

Lange T; Shparlinski I, 2005, 'Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves', Applicable Algebra in Engineering Communications and Computing, 15, pp. 329 - 337, http://dx.doi.org/10.1007/s00200-004-0161-9

Banks WD; Heath-Brown R; Shparlinski IE, 2005, 'On the average value of divisor sums in arithmetic progressions', International Mathematics Research Notices, pp. 1 - 25, http://dx.doi.org/10.1155/imrn.2005.1

Lange T; Shparlinski IE, 2005, 'Certain exponential sums and random walks on elliptic curves', Canadian Journal of Mathematics, 57, pp. 338 - 350, http://dx.doi.org/10.4153/CJM-2005-015-8

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Exponential sums and congruences with factorials', Journal Fur Die Reine Und Angewandte Mathematik, pp. 29 - 44, http://dx.doi.org/10.1515/crll.2005.2005.584.29

Friedlander JB; Pomerance C; Shparlinski IE, 2005, 'Finding the group structure of elliptic curves over finite fields', Bulletin of the Australian Mathematical Society, 72, pp. 251 - 263, http://dx.doi.org/10.1017/s0004972700035048

Contini S; Shparlinski IE, 2005, 'On Stern's attack against secret truncated linear congruential generators', Lecture Notes in Computer Science, 3574, pp. 52 - 60, http://dx.doi.org/10.1007/11506157_5

Luca F; Shparlinski IE, 2005, 'On the largest prime factor of n! + 2n − 1', Journal De Theorie Des Nombres De Bordeaux, 17, pp. 859 - 870, http://dx.doi.org/10.5802/jtnb.524

Shparlinski IE, 2005, 'On the nonlinearity of the sequence of signs of Kloosterman sums', Bulletin of the Australian Mathematical Society, 71, pp. 405 - 409, http://dx.doi.org/10.1017/s0004972700038405

De Koninck JM; Luca F; Shparlinski IE, 2005, 'Powerful numbers in short intervals', Bulletin of the Australian Mathematical Society, 71, pp. 11 - 16, http://dx.doi.org/10.1017/s0004972700037953

Everest G; Shparlinski IE, 2005, 'Prime divisors of sequences associated to elliptic curves', Glasgow Mathematical Journal, 47, pp. 115 - 122, http://dx.doi.org/10.1017/S0017089504002113

Luca F; Shparlinski IE, 2005, 'Prime divisors of shifted factorials', Bulletin of the London Mathematical Society, 37, pp. 809 - 817, http://dx.doi.org/10.1112/S0024609305004923

Hallgren S; Russell A; Shparlinski IE, 2005, 'Quantum noisy rational function reconstruction', Lecture Notes in Computer Science, 3595, pp. 420 - 429, http://dx.doi.org/10.1007/11533719_43

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, 'Uniform Distribution of the Fractional Part of the Average Prime Divisor', Forum Mathematicum, 17, pp. 885 - 901, http://dx.doi.org/10.1515/form.2005.17.6.885

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Waring problem with factorials', Bulletin of the Australian Mathematical Society, 71, pp. 259 - 264, http://dx.doi.org/10.1017/s0004972700038223

Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over F_P and residue races', JOURNAL OF NUMBER THEORY, 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

Garaev MZ; Luca F; Shparlinski IE, 2004, 'Character sums and congruences with n!', Transactions of the American Mathematical Society, 356, pp. 5089 - 5102, http://dx.doi.org/10.1090/S0002-9947-04-03612-8

Dewar M; Panario D; Shparlinski IE, 2004, 'Distribution of exponential functions with k-full exponent modulo a prime', Indagationes Mathematicae, 15, pp. 497 - 503, http://dx.doi.org/10.1016/S0019-3577(04)80014-4

Vasco MIG; Näslund M; Shparlinski IE, 2004, 'New results on the hardness of diffie-hellman bits', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2947, pp. 159 - 172

Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3357, pp. 241 - 251

Banks WD; Harcharras A; Shparlinski IE, 2004, 'Smooth values of shifted primes in arithmetic progressions', Michigan Mathematical Journal, 52, pp. 603 - 618, http://dx.doi.org/10.1307/mmj/1100623415

Shparlinski IE, 2004, 'On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA', Information Processing Letters, 92, pp. 143 - 147, http://dx.doi.org/10.1016/j.ipl.2004.07.004

Shparlinski IE, 2004, 'Bounds of Gauss sums in finite fields', Proceedings of the American Mathematical Society, 132, pp. 2817 - 2824, http://dx.doi.org/10.1090/S0002-9939-04-07133-3

Chou WS; Shparlinski IE, 2004, 'On the cycle structure of repeated exponentiation modulo a prime', Journal of Number Theory, 107, pp. 345 - 356, http://dx.doi.org/10.1016/j.jnt.2004.04.005

Goresky M; Klapper A; Murty R; Shparlinski I, 2004, 'On decimations of ℓ-sequences', SIAM Journal on Discrete Mathematics, 18, pp. 130 - 140, http://dx.doi.org/10.1137/S0895480102403428

Shparlinski IE, 2004, 'Distribution of exponential functions with squarefull exponent in residue rings', Indagationes Mathematicae, 15, pp. 283 - 289, http://dx.doi.org/10.1016/S0019-3577(04)90020-1

Von Zur Gathen J; Shparlinski IE, 2004, 'Polynomial Interpolation from Multiples', Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, 15, pp. 1125 - 1130

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