By Professor Igor Shparlinski

Journal articles

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 F-P and residue races', JOURNAL OF NUMBER THEORY, 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

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

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

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Mov attack in various subgroups on elliptic curves', ILLINOIS JOURNAL OF MATHEMATICS, 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

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

Conflitti A; Shparlinski IE, 2004, 'On the multidimensional distribution of the subset sum generator of pseudorandom numbers', Mathematics of Computation, 73, pp. 1005 - 1011, http://dx.doi.org/10.1090/S0025-5718-03-01563-1

Frandsen GS; Shparlinski IE, 2004, 'On Reducing a System of Equations to a Single Equation', BRICS Report Series, 11, http://dx.doi.org/10.7146/brics.v11i6.21831

Shparlinski IE; Winterhof A, 2004, 'A nonuniform algorithm for the hidden number problem in subgroups', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2947, pp. 416 - 424, http://dx.doi.org/10.1007/978-3-540-24632-9_30

Banks WD; Shparlinski IE, 2004, 'Arithmetic properties of numbers with restricted digits', Acta Arithmetica, 112, pp. 313 - 332, http://dx.doi.org/10.4064/aa112-4-1

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