Publications
Stochastic Calculus for the Theta Process (with Zachary Selk). Submitted. arXiv: 2406.05523
Bounds for Smooth Theta Sums with Rational Parameters (with Tariq Osman). Submitted. arXiv: 2306.11119
Rough Paths above Weierstrass Functions (with Zachary Selk). To appear in Comptes Rendus - Série Mathématique.
Heavy Tailed and Compactly Supported Distributions of Quadratic Weyl Sums with Rational Parameters (with Tariq Osman). Submitted. arXiv: 2210.09838.
Improved Tail Estimates for the Distribution of Quadratic Weyl Sums (with Jory Griffin and Tariq Osman). Special issue "Advances in Dynamical systems by the DinAmicI group" of the Bollettino dell'Unione Matematica Italiana, 16, 2, 2023. Featured as “Editor Top Pick article” for 2023.
Smooth arithmetical sums over k-free integers (with Ram M. Murty). Journal of the Ramanujan Mathematical Society, 36, 2, 2021.
Autocorrelation functions for quantum particles in supersymmetric Pöschl-Teller Potentials. Canadian Mathematical Bulletin, 1-13, 2020. doi:10.4153/S0008439520000879.
The work of Yakov G. Sinai (with Leonid Bunimovich, Boris M. Gurevich, Dong Li, Konstantin M. Khanin, Yakov B. Pesin, Nándor Simányi, and Domokos Szász). The Abel Prize 2013–2017, edited by H. Holden and R. Piene, Springer, 2019.
Ergodic and Statistical Properties of B-Free Numbers (with Maria Avdeeva and Yakov G. Sinai). Theory of Probability and its Applications, 61, 4, 2017.
Quadratic Weyl Sums, Automorphic Functions, and Invariance Principles (with Jens Marklof). Proceeding of the London Mathematical Society, 113, 6, 2016.
On two Conjectures for M&m Sequences (with Sara Munday). Journal of Difference Equations and Applications, 2, 3, 428–440, 2016.
The Abel Prize Award to Ya.G. Sinai (with Alexander I. Bufetov, Boris M. Gurevich, Konstantin M. Khanin). Uspehi Matematicheskikh Nauk, 69, 5 (419), 167–190. English translation in Russian Mathematical Surveys, 69, 5, 931–956. 2014.
Continued Fraction Digit Averages and Maclaurin’s Inequalities (with Douglas Hensley, Steven J. Miller and Jake L. Wellens). Experimental Mathematics, 24, 1, 23–44, 2015.
Ergodic Properties of k-Free Integers in Number Fields (with Ilya Vinogradov). Journal of Modern Dynamics, 7, 3, 461–488, 2013.
Smooth Sums over Smooth k-Free numbers and Statistical Mechanics. Moscow Journal of Combinatorics and Number Theory, 3, 2, 144–180, 2013.
Ergodic Properties of Square-Free Numbers (with Yakov G. Sinai). Journal of the European Mathematical Society, 15, 1343–1374, 2013.
The Möbius Function and Statistical Mechanics (with Yakov G. Sinai). Bulletin of Mathematical Sciences, DOI 10.1007/s13373-011-0011-6, 2011.
Non-Standard Limit Theorems in Number Theory (with Yakov G. Sinai). Prokhorov and Contemporary Probability Theory, Springer Proceedings in Mathematics & Statistics, 33, 197–213, 2013.
On the Curlicue Measures for Theta Sums. Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, 47, 2, 466-497, 2011.
Renewal-type Limit Theorem for Continued Fractions with even partial quotients. Ergodic Theory and Dynamical Systems, 29, 5, pp 1451-1478, 2009.