Exponential sums over Möbius convolutions with applications to partitions
Abstract We establish bounds for exponential sums twisted by generalized Möbius functions and their convolutions. As an application, we prove asymptotic formulas for certain weighted chromatic partitions by using the Hardy–Littlewood circle method. Lastly, we provide an explicit formula relating the contributions from the major arcs with a sum over the zeros of the Riemann zeta-function.
Authors
- Nicolas Robles (ORCID: https://orcid.org/0000-0002-8369-4516)
- Debmalya Basak (ORCID: https://orcid.org/0000-0001-5262-3478)
- Alexandru Zaharescu (ORCID: https://orcid.org/0000-0001-5587-9938)
Institutions
- RAND Corporation (US)
- University of Illinois Urbana-Champaign (US)
- University of Illinois System (US)
- Romanian Academy (RO)
Publication Details
- Journal
- Canadian Journal of Mathematics
- Published
- 2025-01-09
- DOI
- https://doi.org/10.4153/s0008414x24000701
- Citations
- 2
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 10.76