Select Publications
Journal articles
2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, 64, http://dx.doi.org/10.1016/j.jco.2020.101542
,2021, 'Weyl sums over integers with digital restrictions', , http://arxiv.org/abs/2105.04835v1
,2021, 'Additive energy and a large sieve inequality for sparse sequences', , http://arxiv.org/abs/2103.12659v2
,2021, 'Energy bounds for modular roots and their applications', , http://arxiv.org/abs/2103.09405v1
,2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743
,2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363
,2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, 8, http://dx.doi.org/10.1007/s40687-021-00249-4
,2021, 'Bounds of some double exponential sums', Journal of Number Theory, 219, pp. 228 - 236, http://dx.doi.org/10.1016/j.jnt.2020.09.020
,2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386
,2021, 'Counting solvable s-unit equations', Proceedings of the American Mathematical Society, 149, pp. 5119 - 5129, http://dx.doi.org/10.1090/proc/15674
,2021, 'Erratum: Value sets of sparse polynomials (Canadian Mathematical Bulletin (2020) 63 (187-196) DOI: 10.4153/xxxx)', Canadian Mathematical Bulletin, http://dx.doi.org/10.4153/S0008439521000928
,2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, 35, pp. 976 - 987, http://dx.doi.org/10.1137/20M1357731
,2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478
,2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, 27, pp. 903 - 917, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
,2021, 'Perfect powers in value sets and orbits of polynomials', New York Journal of Mathematics, 27, pp. 903 - 917
,2020, 'Two-dimensional Weyl sums failing square-root cancellation along lines', , http://arxiv.org/abs/2012.08877v1
,2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, http://dx.doi.org/10.1016/j.aim.2020.107369
,2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, 68, http://dx.doi.org/10.1016/j.ffa.2020.101747
,2020, 'Metric theory of Weyl sums', , http://arxiv.org/abs/2011.09306v1
,2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, 34, pp. 2124 - 2136, http://dx.doi.org/10.1137/20M1325502
,2020, 'New estimates for exponential sums over multiplicative subgroups and intervals in prime fields', Journal of Number Theory, 215, pp. 261 - 274, http://dx.doi.org/10.1016/j.jnt.2020.02.004
,2020, 'On the distribution of modular square roots of primes', , http://arxiv.org/abs/2009.03460v1
,2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, 214, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023
,2020, 'On large values of Weyl sums', Advances in Mathematics, 370, http://dx.doi.org/10.1016/j.aim.2020.107216
,2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, 293, pp. 1505 - 1514, http://dx.doi.org/10.1002/mana.201900006
,2020, 'Counting solvable $S$-unit equations', , http://arxiv.org/abs/2007.15170v1
,2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001
,2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, 71, pp. 637 - 648, http://dx.doi.org/10.1093/qmathj/haz055
,2020, 'Polynomial Equations in Subgroups and Applications', , http://arxiv.org/abs/2005.05315v1
,2020, 'An effective local-global principle for algebraic varieties and the sum product problem in finite fields', , http://arxiv.org/abs/2005.02923v3
,2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7
,2020, 'Metric theory of lower bounds on Weyl sums', , http://arxiv.org/abs/2004.02539v3
,2020, 'Hybrid bounds on two-parametric family Weyl sums along smooth curves', , http://arxiv.org/abs/2003.02419v1
,2020, 'Value Sets of Sparse Polynomials', Canadian Mathematical Bulletin, 63, pp. 187 - 196, http://dx.doi.org/10.4153/S0008439519000316
,2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, 6, http://dx.doi.org/10.1007/s40993-020-0191-9
,2020, 'Unlikely intersections over finite fields: Polynomial orbits in small subgroups', Discrete and Continuous Dynamical Systems- Series A, 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070
,2020, 'Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers', , http://arxiv.org/abs/2001.09721v1
,2020, 'On digits of Mersenne numbers', , http://arxiv.org/abs/2001.03380v4
,2020, 'Level curves of rational functions nd unimodular points on rational curves', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928
,2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, 148, pp. 2371 - 2377, http://dx.doi.org/10.1090/proc/14901
,2020, 'Sums of algebraic trace functions twisted by arithmetic functions', Pacific Journal of Mathematics, 304, pp. 505 - 522, http://dx.doi.org/10.2140/pjm.2020.304.505
,2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737
,2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369
,2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, pp. 1 - 21, http://dx.doi.org/10.1007/s40993-020-0191-9
,2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, 21, pp. 931 - 941, http://dx.doi.org/10.2422/2036-2145.201811_007
,2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7
,2020, 'Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$', Mathematics of Computation, 322, pp. 911 - 922, http://dx.doi.org/10.1090/mcom/3467
,2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023
,2020, 'Kloosterman paths of prime powers moduli, II', Bulletin de la Societe Mathematique de France, 148, pp. 173 - 188, http://dx.doi.org/10.24033/bsmf.2802
,2020, 'Kloosterman sums with twice-differentiable functions', Functiones et Approximatio Commentarii Mathematici, 63, pp. 113 - 124, http://dx.doi.org/10.7169/facm/1845
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