Welcome!
I am currently a final year PhD student in the Department of Mathematics at the University of Georgia. I am working under the direction of Prof. Paul Pollack, and hope to receive my PhD by April 2025. Hence, I am currently on the job market. I completed my undergraduate studies at the Chennai Mathematical Institute, where I obtained a BSc. Honors in Mathematics and Computer Science.
My primary research interests lie in elementary, analytic and combinatorial number theory. In part of my thesis, I obtain new results on the distribution in arithmetic progressions of values taken by arithmetic functions: This was born out of a series of joint papers with my advisor and his former student Dr. Noah Lebowitz-Lockard, – where we had set out to investigate analogues of the Siegel-Walfisz theorem for large classes of additive and multiplicative functions as well as for the joint distribution of families consisting of such functions, – and recently culminated in three solo papers obtaining some of the best possible results in this direction.
My current research (which constitutes the second part of my thesis) concerns new results on mean values of multiplicative functions as well as various new applications of these results. Besides these, I have coauthored multiple papers with my advisor, and with Profs. Vorrapan (Fai) Chandee, Xiannan Li and Nathan McNew, on a variety of topics such as Benford’s law (studying this phenomenon for various interesting sequences such as Hecke eigenvalues of newforms), distributions of intermediate prime factors and the behavior of the famous “aliquot sum” function $s(n)$. I am also interested in a variety of other questions on the “anatomy of integers”, Erdos-type problems and general statistical questions on distributions of arithmetic functions, including Fourier coefficients of modular forms and the partition function.
My research blends several areas of mathematics beyond my aforementioned primary interests, such as linear algebra and module theory, probability, commutative algebra, algebraic number theory, as well as arithmetic and algebraic geometry. Moreover, my work relies heavily on character sums and exponential sums, and many of the questions I have worked on and am working on have interesting analogues in the realms of $L$-functions, modular forms (and more generally automorphic forms), probability and probabilistic number theory. As part of my research, I have used multiple mathematical software packages such as Sage, Pari/GP, Macaulay2, and Magma.
I am the 2024 recipient of the William Armor Wills Memorial Scholarship Award from the Department of Mathematics at UGA.
Emails:
akash01s.roy@gmail.com
Akash.SinghaRoy@uga.edu
Office: Boyd Research and Education Center, 427J