AkashSinghaRoy

Research: Publications, Preprints and Talks

PhD Dissertation

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

  12. Anatomical mean value bounds on multiplicative functions and the distribution of the sum of divisors
    Michigan Math. J., accepted for publication.
    Link: Most recent version

Completed/Submitted Papers

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

  2. Joint distribution in residue classes of families of multiplicative functions I
    Submitted to Int. Math. Res. Not.
    Link: Most recent version

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

  4. The Landau-Selberg-Delange method for products of Dirichlet $L$-functions, and applications, I.
    Link: Most recent version

Manuscripts under preparation

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

  2. Mean values of multiplicative functions in (generalized) 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/Arithmetic Geometry Seminar (April 2024)
    Joint distribution in residue classes of families of “polynomially-defined” multiplicative functions   Slides

  3. Dartmouth College Algebra and Number Theory Seminar (November 2024)
    Distribution and mean values of families of multiplicative functions in arithmetic progressions   Slides

  4. University of Waterloo Number Theory Seminar (January 2025)
    Residue-class distribution and mean values of multiplicative functions   Slides

  5. AMS Spring Eastern Sectional Meeting 2025: Special session on Counting and Asymptotics in Number Theory (April 2025)
    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 functions   Slides

  7. Combinatorial and Additive Number Theory CANT 2025 (May 2025)
    Joint distribution in residue classes of families of multiplicative functions

  8. ELAZ 2026, Conference on elementary and analytic number theory (February 2026)
    The Landau-Selberg-Delange method for Dirichlet L-functions, and applications   Slides

  9. Charles University (Univerzita Karlova) Number Theory Seminar (March 2026)
    The Landau-Selberg-Delange method for Dirichlet L-functions, and applications   Slides

  10. Simons Summer School and Workshop on Discrete Harmonic Analysis and Analytic Number Theory (May 2026)
    The Landau-Selberg-Delange method for Dirichlet L-functions, and applications