By Professor Igor Shparlinski

Journal articles

Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, 'Interpolation and approximation of polynomials in finite fields over a short interval from noisy values', Experimental Mathematics, 23, pp. 241 - 260, http://dx.doi.org/10.1080/10586458.2014.890918

Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9

Shparlinski IE; Sutantyo D, 2014, 'Distribution of elliptic twin primes in isogeny and isomorphism classes', Journal of Number Theory, 137, pp. 1 - 15, http://dx.doi.org/10.1016/j.jnt.2013.10.018

Luca F; Shparlinski IE, 2014, 'On the counting function of elliptic carmichael numbers', Canadian Mathematical Bulletin, 57, pp. 105 - 112, http://dx.doi.org/10.4153/CMB-2012-037-4

Shparlinski IE, 2014, 'On the distribution of points on the generalized markoff-hurwitz and dwork hypersurfaces', International Journal of Number Theory, 10, pp. 151 - 160, http://dx.doi.org/10.1142/S1793042113500863

Chen Z; Shparlinski IE; Winterhof A, 2014, 'Covering sets for limited-magnitude errors', IEEE Transactions on Information Theory, 60, pp. 5315 - 5321, http://dx.doi.org/10.1109/TIT.2014.2338078

Shparlinski IE, 2014, 'Distribution of exponential functions modulo a prime power', Journal of Number Theory, 143, pp. 224 - 231, http://dx.doi.org/10.1016/j.jnt.2014.04.010

Chang MC; Kerr B; Shparlinski IE; Zannier U, 2014, 'Elements of large order on varieties over prime finite fields', Journal de Theorie des Nombres de Bordeaux, 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880

Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, 547, pp. 117 - 121, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Ahmadi O; Shparlinski IE, 2014, 'Exponential sums over points of elliptic curves', Journal of Number Theory, 140, pp. 299 - 313, http://dx.doi.org/10.1016/j.jnt.2014.01.016

Shparlinski IE, 2014, 'Multiple exponential and character sums with monomials', Mathematika, 60, pp. 363 - 373, http://dx.doi.org/10.1112/S0025579314000084

Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809

Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, 89, pp. 300 - 307, http://dx.doi.org/10.1017/S0004972713000671

Ling S; Shparlinski I; Wang H, 2014, 'On the multidimensional distribution of the Naor-Reingold pseudo-random function', Mathematics of Computation, 83, pp. 2429 - 2434, http://dx.doi.org/10.1090/S0025-5718-2014-02794-4

Shparlinski IE, 2014, 'Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields', Journal of Symbolic Computation, 64, pp. 35 - 41, http://dx.doi.org/10.1016/j.jsc.2013.12.005

Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, 70, pp. 301 - 325

Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv der Mathematik, 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0

Blake IF; Luca F; Shparlinski IE, 2014, 'VSH and multiplicative modular relations between small primes with polynomial exponents', Applicable Algebra in Engineering, Communications and Computing, 25, pp. 181 - 188, http://dx.doi.org/10.1007/s00200-014-0219-2

Shparlinski IE; Sutherland AV, 2014, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, pp. 1 - 13, http://dx.doi.org/10.1007/s10208-013-9181-9

Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470

Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011

Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022

Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8

Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, 24, pp. 930 - 938, http://dx.doi.org/10.1016/j.indag.2013.02.005

Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte fur Mathematik, 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x

Shparlinski IE, 2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, 67, pp. 55 - 61, http://dx.doi.org/10.1007/s10998-013-2736-3

Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012

Shparlinski IE, 2013, 'On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves', Michigan Mathematical Journal, 62, pp. 491 - 505, http://dx.doi.org/10.1307/mmj/1378757885

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2013, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, http://dx.doi.org/10.1016/j.jctb.2015.07.003

Shparlinski IE, 2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, 43, pp. 361 - 371, http://dx.doi.org/10.1216/RMJ-2013-43-1-361

Shparlinski I, 2013, 'Erratum: Sum-product estimates and multiplicative orders ofΓ and Γ + Γ^-1 in finite fields (Bulletin of the Australian Mathematical Society)', Bulletin of the Australian Mathematical Society, 87, pp. 527 - 528, http://dx.doi.org/10.1017/S0004972712001062

Heyman R; Shparlinski IE, 2013, 'On the number of Eisenstein polynomials of bounded height', Applicable Algebra in Engineering, Communications and Computing, 24, pp. 149 - 156, http://dx.doi.org/10.1007/s00200-013-0187-y

Gutierrez J; Ibeas A; Gómez-Pérez D; Shparlinski IE, 2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs, Codes, and Cryptography, 67, pp. 395 - 402, http://dx.doi.org/10.1007/s10623-012-9615-4

Shparlinski IE, 2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, 25, pp. 647 - 664, http://dx.doi.org/10.1515/FORM.2011.141

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2013, 'On congruences with products of variables from short intervals and applications', Proceedings of the Steklov Institute of Mathematics, 280, pp. 61 - 90, http://dx.doi.org/10.1134/S0081543813010057

Shparlinski IE, 2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, 36, pp. 99 - 108, http://dx.doi.org/10.2996/kmj/1364562722

Shparlinski IE, 2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, 113, pp. 414 - 417, http://dx.doi.org/10.1016/j.ipl.2013.03.016

Shparlinski IE, 2013, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Shparlinski IE, 2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, 66, pp. 65 - 90, http://dx.doi.org/10.1007/978-1-4614-5389-5_4

Baker RC; Banks WD; Brüdern J; Shparlinski IE; Weingartner AJ, 2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3

Farashahi RR; Fouque PA; Shparlinski IE; Tibouchi M; Voloch JF, 2013, 'Indifferentiable deterministic hashing to elliptic and hyperelliptic curves', Mathematics of Computation, 82, pp. 491 - 512, http://dx.doi.org/10.1090/S0025-5718-2012-02606-8

Shparlinski IE; Winterhof A, 2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, 19, pp. 93 - 104, http://dx.doi.org/10.1016/j.ffa.2012.10.004

Borwein JM; Shparlinski I; Zudilin W, 2013, 'Number Theory and Related Fields: In Memory of Alf van der Poorten', Springer Proceedings in Mathematics and Statistics, 43

Cilleruelo J; Kumchev A; Luca F; Rué J; Shparlinski IE, 2013, 'On the fractional parts of aⁿ/n', Bulletin of the London Mathematical Society, 45, pp. 249 - 256, http://dx.doi.org/10.1112/blms/bds084

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, 'On the hidden shifted power problem', SIAM Journal on Computing, 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414

Shparlinski IE; Stange KE, 2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x

Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7

Shparlinski IE, 2012, 'Modular hyperbolas', Japanese Journal of Mathematics, 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8

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