By Professor Igor Shparlinski

Journal articles

Banks WD; Friedlander JB; Luca F; Pappalardi F; Shparlinski IE, 2006, 'Coincidences in the values of the Euler and Carmichael functions', Acta Arithmetica, 122, pp. 207 - 234, http://dx.doi.org/10.4064/aa122-3-1

Garaev MZ; Luca F; Shparlinski IE, 2006, 'Catalan and Apéry numbers in residue classes', Journal of Combinatorial Theory. Series A, 113, pp. 851 - 865, http://dx.doi.org/10.1016/j.jcta.2005.08.003

Garaev MZ; Luca F; Shparlinski IE; Winterhof A, 2006, 'On the lower bound of the linear complexity over Fp of Sidelnikov sequences', IEEE Transactions on Information Theory, 52, pp. 3299 - 3304, http://dx.doi.org/10.1109/TIT.2006.876352

Blackburn SR; Shparlinski IE, 2006, 'Character sums and nonlinear recurrence sequences', Discrete Mathematics, 306, pp. 1126 - 1131, http://dx.doi.org/10.1016/j.disc.2006.02.012

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Character sums with exponential functions over smooth numbers', Indagationes Mathematicae, 17, pp. 157 - 168, http://dx.doi.org/10.1061/(ASCE)0733-9372(2006)132:2(157)

Coppersmith D; Howgrave-Graham N; Nguyễn PQ; Shparlinski IE, 2006, 'Testing set proportionality and the Ádám isomorphism of circulant graphs', Journal of Discrete Algorithms, 4, pp. 324 - 335, http://dx.doi.org/10.1016/j.jda.2005.06.003

Shparlinski IE, 2006, 'Truncations of L-functions in residue classes', Glasgow Mathematical Journal, 48, pp. 347 - 350, http://dx.doi.org/10.1017/S0017089506003120

Contini S; Croot E; Shparlinski IE, 2006, 'Complexity of inverting the Euler function', Mathematics of Computation, 75, pp. 983 - 996, http://dx.doi.org/10.1090/S0025-5718-06-01826-6

Banks WD; Shparlinski IE, 2006, 'Multiplicative character sums with the sum of g-ary digits function', Ramanujan Journal, 11, pp. 215 - 219, http://dx.doi.org/10.1007/s11139-006-6508-z

Shparlinski IE, 2006, 'On RSA moduli with prescribed bit patterns', Designs, Codes, and Cryptography, 39, pp. 113 - 122, http://dx.doi.org/10.1007/s10623-005-3137-2

Shparlinski IE, 2006, 'On some generalisations of the Erdos distance problem over finite fields', Bulletin of the Australian Mathematical Society, 73, pp. 285 - 292, http://dx.doi.org/10.1017/S0004972700038867

Shparlinski I, 2006, 'On the energy of some circulant graphs', Linear Algebra and Its Applications, 414, pp. 378 - 382, http://dx.doi.org/10.1016/j.laa.2005.10.020

Shparlinski IE; Winterhof A, 2006, 'On the nonlinearity of linear recurrence sequences', Applied Mathematics Letters, 19, pp. 340 - 344, http://dx.doi.org/10.1016/j.aml.2005.04.015

Banks WD; Friedlander JB; Konyagin SV; Shparlinski IE, 2006, 'Incomplete exponential sums and Diffie-Hellman triples', Mathematical Proceedings of the Cambridge Philosophical Society, 140, pp. 193 - 206, http://dx.doi.org/10.1017/S0305004105008947

Shparlinski IE, 2006, 'On the sum of iterations of the Euler function', Journal of Integer Sequences, 9, pp. 1 - 5

Banks WD; Shparlinski IE, 2006, 'Integers with a large smooth divisor', , http://arxiv.org/abs/math/0601460v1

Luca F; Shparlinski IE, 2006, 'Arithmetic properties of the Ramanujan function', Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 116, pp. 1 - 8, http://dx.doi.org/10.1007/BF02829735

Banks WD; Luca F; Shparlinski IE, 2006, 'Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n', Commentarii Mathematici Helvetici, 81, pp. 1 - 22, http://dx.doi.org/10.4171/CMH/40

Banks WD; Luca F; Shparlinski IE, 2006, 'Common divisors of the Euler function at related arguments', ACTA SCIENTIARUM MATHEMATICARUM, 72, pp. 525 - 536, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000216758800005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Double character sums over elliptic curves and finite fields', PURE AND APPLIED MATHEMATICS QUARTERLY, 2, pp. 179 - 197, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000241377300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Exponential sums with Dickson polynomials', Finite Fields and their Applications, 12, pp. 16 - 25, http://dx.doi.org/10.1016/j.ffa.2004.08.001

Banks WD; Shparlinski IE, 2006, 'Non-residues and primitive roots in beatty sequences', Bulletin of the Australian Mathematical Society, 73, pp. 433 - 443, http://dx.doi.org/10.1017/s0004972700035449

Blake IF; Garefalakis T; Shparlinski IE, 2006, 'On the bit security of the Diffie-Hellman key', Applicable Algebra in Engineering, Communications and Computing, 16, pp. 397 - 404, http://dx.doi.org/10.1007/s00200-005-0184-x

Shparlinski IE; Winterhof A, 2006, 'On the discrepancy and linear complexity of some counter-dependent recurrence sequences', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4086 LNCS, pp. 295 - 303, http://dx.doi.org/10.1007/11863854_25

Banks WD; Shparlinski IE, 2006, 'Short character sums with beatty sequences', Mathematical Research Letters, 13, pp. 539 - 547, http://dx.doi.org/10.4310/MRL.2006.v13.n4.a4

Luca F; McKee J; Shparlinsk IE, 2006, 'Small exponent point groups on elliptic curves', Journal de Theorie des Nombres de Bordeaux, 18, pp. 471 - 476, http://dx.doi.org/10.5802/jtnb.554

Banks WD; Shparlinski IE, 2006, 'Average Value of the Euler Function on Binary Palindromes', Bulletin of the Polish Academy of Sciences Mathematics, 54, pp. 95 - 101, http://dx.doi.org/10.4064/ba54-2-1

Banks MK, 2006, 'Editor’s Note', Journal of Environmental Engineering, 132, pp. 157 - 157, http://dx.doi.org/10.1061/(asce)0733-9372(2006)132:2(157)

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 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

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