Graduate Student PhD candidate (graduated) Instructor of record IMPORTANT UPDATE:Starting from October 2025, I will be a postdoctoral fellow in the number theory research group UFOCLAN at Charles University, Prague. My UGA directory page (i.e. this page) may stop existing, so my most recent updates (especially research updates) will be present only on my website (URL: https://akashsingharoy.github.io/). My UGA email (Akash.SinghaRoy@uga.edu) will stop being valid within a few months, however I will continue to regularly check my permanent email: akash01s.roy@gmail.com. Welcome! As of July 2025, I have completed my Ph.D. in Mathematics at the University of Georgia under the direction of Paul Pollack. I completed my undergraduate studies at the Chennai Mathematical Institute in July 2021, where I obtained a BSc. Honors in Mathematics and Computer Science. My primary research interests lie in elementary, analytic and combinatorial number theory. In my Ph.D. thesis, I study the residue-class distribution of (families of) arithmetic functions to varying moduli: More precisely, I obtain new analogues of the Siegel-Walfisz theorem for large classes of additive and multiplicative functions, which are essentially optimal in many ways. This work blends ideas that could be thought of as being borrowed from probability (but executed via methods from the "anatomy of integers"), with machinery from linear algebra over rings (a.k.a. module theory), classical analytic number theory, character sums/exponential sums, commutative algebra, as well as arithmetic and algebraic geometry. I am currently working on a variety of new projects. In one of these projects (which is almost complete!), I give new results on mean values of multiplicative functions that extend the classical Landau-Selberg-Delange "LSD" method to situations where the Dirichlet series under consideration is controlled by Dirichlet $L$-functions mod $q$ (instead of the usual Riemann zeta function); my results allow the conductor $q$ to vary within ranges that are typically much wider than those permitted by known forms of the "LSD" method. More updates on other projects coming soon! Besides these, I have coauthored papers with Vorrapan (Fai) Chandee, Xiannan Li, Nathan McNew and Paul Pollack on topics such as (i) Benford's law (studying this phenomenon for various sequences of interest such as Hecke eigenvalues of newforms), (ii) Distributions of intermediate prime factors, and (iii) Behavior of the "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. I am the 2024 recipient of the William Armor Wills Memorial Scholarship Award from the Department of Mathematics at UGA. Please see my webpage for more details (and recent details) on my research, teaching and service/outreach activities. Research Research Areas: Number Theory and Arithmetic Geometry Research Interests: My primary research interests lie in elementary, analytic and combinatorial number theory. In my Ph.D. thesis, I study the residue-class distribution of (families of) arithmetic functions to varying moduli: More precisely, I obtain new analogues of the Siegel-Walfisz theorem for large classes of additive and multiplicative functions, which are essentially optimal in many ways. This work blends ideas that could be thought of as being borrowed from probability (but executed via methods from the "anatomy of integers"), with machinery from linear algebra over rings (a.k.a. module theory), classical analytic number theory, character sums/exponential sums, commutative algebra, as well as arithmetic and algebraic geometry. I am currently working on a variety of new projects. In one of these projects (which is almost complete!), I give new results on mean values of multiplicative functions that extend the classical Landau-Selberg-Delange "LSD" method to situations where the Dirichlet series under consideration is controlled by Dirichlet $L$-functions mod $q$ (instead of the usual Riemann zeta function); my results allow the conductor $q$ to vary within ranges that are typically much wider than those permitted by known forms of the "LSD" method. More updates on other projects coming soon! Besides these, I have coauthored papers with Vorrapan (Fai) Chandee, Xiannan Li, Nathan McNew and Paul Pollack on topics such as (i) Benford's law (studying this phenomenon for various sequences of interest such as Hecke eigenvalues of newforms), (ii) Distributions of intermediate prime factors, and (iii) Behavior of the "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. I am the 2024 recipient of the William Armor Wills Memorial Scholarship Award from the Department of Mathematics at UGA. Dissertation/Thesis Title: Residue-class distribution of arithmetic functions to varying moduli Degree Completion Date: Tue, 04/15/2025 - 12:00pm Selected Publications Selected Publications: Published, Accepted and submitted Works (Oldest first) 1. Steps into analytic number theory: A problem-based introduction (with P. Pollack) Springer, Problem Books in Mathematics, 2021. 2. Distribution mod $p$ of Euler's totient and the sum of proper divisors (with N. Lebowitz-Lockard and P. Pollack)Michigan Math. J. 74 (2024), 143–166.Links: Journal arXiV 3. Joint distribution in residue classes of polynomial-like multiplicative functions (with P. Pollack) Acta Arith. 202 (2022), 89–104.Link: Journal arXiV 4. Powerfree sums of proper divisors (with P. Pollack)Colloq. Math 168 (2022), 287–295.Link: Journal arXiV 5. Dirichlet, Sierpinski, and Benford (with P. Pollack)J. Number Theory 239 (2022), 352–364.Link: Journal 6. On Benford's Law for multiplicative functions (with V. Chandee, X. Li and P. Pollack)Proc. Amer. Math. Soc. 151 (2023), 4607–4619.Link: Journal arXiV 7. Benford behavior and distribution in residue classes of large prime factors (with P. Pollack)Canad. Math. Bull. 66 (2023), 626–642.Link: Journal 8. Distribution in coprime residue classes of polynomially-defined multiplicative functions (with P. Pollack)Math. Z. 303 (2023), no. 4, paper 93, 20 pages.Link: Journal (older) arXiV 9. Intermediate prime factors in specified subsets (with N. McNew and P. Pollack)Monatsh. Math. 202 (2023), 837–855.Link: Journal 10. The distribution of intermediate prime factors (with N. McNew and P. Pollack)Illinois J. Math. 68 (2024), no. 3, 537-576. Link: Journal arXiV 11. Mean values of multiplicative functions and applications to residue-class distribution (with P. Pollack)Proc. Edinb. Math. Soc., accepted for publication.Link: Most recent version 12. Anatomical mean value bounds on multiplicative functions and the distribution of the sum of divisors, 34 pages Michigan Math. J., accepted for publication.Link: Most recent version 13. Joint distribution in residue classes of families of polynomially-defined additive functions, 34 pagesSubmitted to Math Z.Link: Most recent version 14. Joint distribution in residue classes of families of polynomially-defined multiplicative functions I, 53 pagesSubmitted to J. London Math. Soc.Link: Most recent version 15. Joint distribution in residue classes of families of polynomially-defined multiplicative functions II, 31 pagesSubmitted to Acta. Arith.Link: Most recent version Manuscripts under preparation 16. The Landau-Selberg-Delange method for products of Dirichlet $L$-functions and applications. 17. Distribution in residue classes of hybrid families of polynomially-defined additive and multiplicative functions. 18. Weighted equidistribution and mean values of multiplicative functions in twisted progressions. recent talks and slides 1. PAlmetto Number Theory Series (PANTS) XXXVII: December 2023Distribution in coprime residue classes of Euler’s totient and the sum of divisorsLink to slides 2. University of Georgia Number Theory Seminar: April 2024Joint distribution in residue classes of families of ``polynomially-defined” multiplicative functionsLink to slides 3. Dartmouth College Algebra and Number Theory Seminar: November 2024Distribution and mean values of families of multiplicative functions in arithmetic progressionsLink to slides 4. University of Waterloo, Number Theory Seminar: January 2025Residue-class distribution and mean values of multiplicative functionsLink to slides 5. AMS Spring Eastern Sectional Meeting 2025: Special session on “Counting and Asymptotics in Number Theory” (April 2025)Joint distribution in residue classes of families of multiplicative functions 6. INTEGERS Conference 2025 at the University of Georgia: In Honor of the 80th Birthdays of Melvyn Nathanson and Carl Pomerance (May 2025)Joint distribution in residue classes of families of multiplicative functionsLink to slides 7. Combinatorial and Additive Number Theory CANT 2025: May 2025Distribution and mean values of families of multiplicative functions in arithmetic progressions Other Information Of note: Recipient of: William Armor Wills Memorial Scholarship Award 2024. UGA Graduate School Dean's Award 2023. UGA Graduate School Research Assistantship: August 2022 to May 2023. Exemplary Counselor Award at Ross/Asia Mathematics Program 2019. Please see CV for list of other awards. Refereeing Have refereed for Monatshefte fur Mathematik. Women in Numbers Europe 4 – Research Directions in Number Theory, Springer, Association for Women in Mathematics Series. Rose-Hulman Undergraduate Mathematics Journal. Courses Regularly Taught: MATH2250 MATH1113 Teaching Teaching: Teaching and service at UGA Fall 2024 Instructor of MATH 2250 (Calculus I)Flipped/hybrid classroom structure. Math Study Hall tutor. Committee for UGA High School Math Tournament 2024Contributed several questions and was involved in the design of the contest. Spring 2024 Instructor of MATH 2250 (Calculus I)Flipped/hybrid classroom structure. Committee for design of MATH 2250 final exam. MATH 2250 Active Learning Working Group. Math Study Hall tutor. Fall 2023 Instructor for MATH 1113 (Precalculus)Flipped classroom structure. Grader for MATH 3100 (Sequences and series)Instructed by Prof. Paul Pollack. Teaching and service prior to UGA Counselor in the Ross/Asia Mathematics program 2019.The Ross Program is a residential summer math camp for high school students, primarily focused on algebra and number theory, where students are immersed in the process of mathematical discovery for six weeks. As a Counselor, my responsibility was to mentor the students by guiding their thinking and providing detailed feedback on their work; in addition, I also discussed several interesting mathematical problems with students and gave several informal lectures. Received Exemplary Counselor Award “in recognition of outstanding work at the 2019 Ross/Asia Mathematics Program”. Served on committee for evaluating applications to the Ross Mathematics Program: 2020-2021. Teaching assistant in the courses Algebra III and Algebra IV at the Chennai Mathematical Institute: 2020-2021. Contributed questions to and served as grader for the Scholastic Test for Excellence in Mathematical Sciences (STEMS) conducted by the Chennai Mathematical Institute: 2019. Junior Counselor in the Ross Mathematics Program at the Ohio State University: 2018.
