By Professor Igor Shparlinski

Journal articles

Saxena N; Severini S; Shparlinski I, 2007, 'Parameters of integral circulant graphs and periodic quantum dynamics', International Journal of Quantum Information, 5, pp. 417 - 430, http://dx.doi.org/10.1142/S0219749907002918

Luca F; Shparlinski IE, 2007, 'Pseudoprime Cullen and Woodall numbers', Colloquium Mathematicum, 107, pp. 35 - 43, http://dx.doi.org/10.4064/cm107-1-5

Balasuriya S; Luca F; Shparlinski IE, 2007, 'Prime Divisors Of Some Recurrence Sequence', Periodica Mathematica Hungarica, 54, pp. 215 - 227, http://dx.doi.org/10.1007/s-10998-007-2215-z

Shparlinski IE; Voloch JF, 2007, 'Visible Points on Curves over Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, 55, pp. 193 - 199, http://dx.doi.org/10.4064/ba55-3-1

Luca F; Shparlinski IE, 2006, 'Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function', Indagationes Mathematicae, 17, pp. 611 - 625, http://dx.doi.org/10.1016/S0019-3577(06)81037-2

Banks WD; Shparlinski IE, 2006, 'Congruences and rational exponential sums with the euler function', Rocky Mountain Journal of Mathematics, 36, pp. 1415 - 1426, http://dx.doi.org/10.1216/rmjm/1181069373

Luca F; Shparlinski IE, 2006, 'On the number of polynomial maps into $\mathbb{Z}_{n}$', Tsukuba Journal of Mathematics, 30, http://dx.doi.org/10.21099/tkbjm/1496165073

Luca F; Shparlinski IE, 2006, 'ON THE NUMBER OF POLYNOMIAL MAPS INTO Z(n)', TSUKUBA JOURNAL OF MATHEMATICS, 30, pp. 431 - 441, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000219852100011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Luca F; Shparlinski IE, 2006, 'Some divisibilities amongst the terms of linear recurrences', Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 76, pp. 143 - 156, http://dx.doi.org/10.1007/BF02960862

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', Journal of Algorithms, 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', JOURNAL OF ALGORITHMS-COGNITION INFORMATICS AND LOGIC, 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002

Shparlinski I, 2006, 'On the set of distances between two sets over finite fields', International Journal of Mathematics and Mathematical Sciences, 2006, http://dx.doi.org/10.1155/IJMMS/2006/59482

Luca F; Shparlinski IE, 2006, 'Elliptic curves with low embedding degree', Journal of Cryptology, 19, pp. 553 - 562, http://dx.doi.org/10.1007/s00145-006-0544-0

Luca F; Shparlinski IE, 2006, 'Uniformity of distribution modulo 1 of the geometric mean prime divisor', Boletin De La Sociedad Matematica Mexicana, 12, pp. 155 - 163

Von Zur Gathen J; Shparlinski IE, 2006, 'GCD of random linear combinations', Algorithmica New York, 46, pp. 137 - 148, http://dx.doi.org/10.1007/s00453-006-0072-1

Garaev MZ; Luca F; Shparlinski IE, 2006, 'Distribution of harmonic sums and Bernoulli polynomials modulo a prime', Mathematische Zeitschrift, 253, pp. 855 - 865, http://dx.doi.org/10.1007/s00209-006-0939-5

El-Mahassni ED; Shparlinski IE; Winterhof A, 2006, 'Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers', Monatshefte Fur Mathematik, 148, pp. 297 - 307, http://dx.doi.org/10.1007/s00605-005-0355-7

Shparlinski IE; Winterhof A, 2006, 'Constructions of approximately mutually unbiased bases', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3887 LNCS, pp. 793 - 799, http://dx.doi.org/10.1007/11682462_72

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/10.1016/s0019-3577(06)80013-3

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

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

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