AkashSinghaRoy

Manuscripts organized by chronology of completion

Book

1. Steps into Analytic Number Theory: A Problem-Based Introduction (with Paul Pollack)
Springer, Problem Books in Mathematics, 2021.

Undergraduate research (January-July 2021)

2. Distribution mod $p$ of Euler’s totient and the sum of proper divisors (with Noah Lebowitz-Lockard and Paul Pollack)
Michigan Mathematical Journal 74 (2024), 143–166.
Links to manuscript: Journal   arXiV

3. Joint distribution in residue classes of polynomial-like multiplicative functions (with Paul Pollack)
Acta Arithmetica 202 (2022), 89–104.
Links to manuscript: Journal   arXiV

4. Powerfree sums of proper divisors (with Paul Pollack)
Colloquium Mathematicum 168 (2022), 287–295.
Links to manuscript: Journal   arXiV

5. Dirichlet, Sierpinski, and Benford (with Paul Pollack)
Journal of Number Theory 239 (2022), 352–364.
Link to manuscript: Journal

Graduate research (February 2022-July 2025)

6. Benford behavior and distribution in residue classes of large prime factors (with Paul Pollack)
Canadian Mathematical Bulletin 66 (2023), 626–642.
Link to manuscript: Journal

7. On Benford’s Law for multiplicative functions (with Vorrapan Chandee, Xiannan Li, and Paul Pollack)
Proceedings of the American Mathematical Society 151 (2023), 4607–4619.
Links to manuscript: Journal   arXiV

8. Distribution in coprime residue classes of polynomially-defined multiplicative functions (with Paul Pollack)
Mathematische Zeitschrift 303 (2023), no. 4, paper 93, 20 pages.
Links to manuscript: Journal   arXiV

9. Intermediate prime factors in specified subsets (with Nathan McNew and Paul Pollack)
Monatshefte für Mathematik 202 (2023), 837–855.
Link to manuscript: Journal

10. The distribution of intermediate prime factors (with Nathan McNew and Paul Pollack)
Illinois Journal of Mathematics 68 (2024), no. 3, 537-576.
Links to manuscript: Journal   arXiV

11. Mean values of multiplicative functions and applications to residue-class distribution (with Paul Pollack)
Proceedings of the Edinburgh Mathematical Society 68 (2025), no. 3, 712-730.
Link to manuscript: Most recent version

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

13. Joint distribution in residue classes of families of polynomially-defined additive functions
Under consideration for publication in Mathematische Zeitschrift
Link to manuscript: Most recent version

14. Joint distribution in residue classes of families of polynomially-defined multiplicative functions
Link to older (thesis) version
This is an older version of the manuscript; it was used in my PhD thesis. A completely rewritten and improved version can be found in the postdoctoral research subsection below.

15. Joint distribution in residue classes of families of polynomially-defined multiplicative functions II
Link to older (thesis) version
This is an older version of the manuscript; it was used in my PhD thesis. A completely rewritten and improved version can be found in the postdoctoral research subsection below.

PhD Dissertation

Postdoctoral research (November 2025+)

14. Joint distribution in residue classes of families of multiplicative functions I, Submitted
This is a completely rewritten version of Manuscript 14 in the graduate research subsection above. This immensely simplifies the arguments and establishes more general results.
Link to manuscript: Most recent version

15. Joint distribution in residue classes of families of multiplicative functions II, Submitted
This is a completely rewritten version of Manuscript 15 in the graduate research subsection above. This immensely simplifies the arguments and establishes more general results.
Link to manuscript: Coming soon

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

17. The Furstenberg-Sárközy theorem for sums of an even number of odd powers (with Alexandros Kalogirou, Andrew Lott, and Akos Magyar)
Completed manuscript; public version will be available soon.

Forthcoming manuscripts

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

19. Joint distribution in residue classes of hybrid families of additive and multiplicative functions.

20. Mean values of multiplicative functions in generalized progressions.