AkashSinghaRoy

Research: Publications, Preprints and Talks

Published and Accepted Works

  1. Steps into analytic number theory: A problem-based introduction (with P. Pollack)
    Springer, Problem Books in Mathematics.

  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   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

Submitted Papers

  1. Joint distribution in residue classes of families of polynomially-defined multiplicative functions I, 53 pages
    Submitted to J. London Math. Soc.
    Link: Most recent version

  2. Joint distribution in residue classes of families of polynomially-defined multiplicative functions II, 31 pages
    Submitted to Acta. Arith.
    Link: Most recent version

  3. Joint distribution in residue classes of families of polynomially-defined additive functions, 34 pages
    Submitted to Math Z.
    Link: Most recent version

  4. Anatomical mean value bounds on multiplicative functions and the distribution of the sum of divisors, 34 pages
    Submitted to Michigan Math. J.
    Link: Most recent version

Manuscripts under preparation

  1. The Landau-Selberg-Delange method for products of Dirichlet $L$-functions and applications.

  2. Distribution in residue classes of hybrid families of polynomially-defined additive and multiplicative functions.

  3. Weighted equidistribution and mean values of multiplicative functions in twisted progressions

Recent Talks and Slides

  1. PAlmetto Number Theory Series (PANTS) XXXVII: December 2023
    Distribution in coprime residue classes of Euler’s totient and the sum of divisors   Slides

  2. University of Georgia Number Theory Seminar: April 2024
    Joint distribution in residue classes of families of arithmetic functions   Slides

  3. Dartmouth College Algebra and Number Theory Seminar: November 2024 (upcoming)
    Equidistribution and mean values of families of multiplicative functions   Slides

  4. AMS Spring Eastern Sectional Meeting 2025: “Counting and Asymptotics in Number Theory” (upcoming, April 2025)