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Select Publications
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
,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
,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
,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
,2014, 'Multiple exponential and character sums with monomials', Mathematika, 60, pp. 363 - 373, http://dx.doi.org/10.1112/S0025579314000084
,2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809
,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
,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
,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
,2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, 70, pp. 301 - 325
,2014, 'Squarefree parts of discriminants of trinomials', Archiv der Mathematik, 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0
,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
,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
,2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470
,2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011
,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
,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
,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
,2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,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
,2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3
,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
,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
,2013, 'Number Theory and Related Fields: In Memory of Alf van der Poorten', Springer Proceedings in Mathematics and Statistics, 43
,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
,2012, 'On the hidden shifted power problem', SIAM Journal on Computing, 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414
,2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x
,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
,2012, 'Modular hyperbolas', Japanese Journal of Mathematics, 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8
,2012, 'On the distribution of solutions to polynomial congruences', Archiv der Mathematik, 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5
,2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2
,2012, 'On numbers n dividing the nth term of a linear recurrence', Proceedings of the Edinburgh Mathematical Society, 55, pp. 271 - 289, http://dx.doi.org/10.1017/S0013091510001355
,2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields', Bulletin of the Australian Mathematical Society, 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887
,2012, 'Random walks and bisections in random circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7256 LNCS, pp. 542 - 555, http://dx.doi.org/10.1007/978-3-642-29344-3_46
,2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, 2012, pp. 1968 - 2009, http://dx.doi.org/10.1093/imrn/rnr097
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