Abstract
We consider colored partitions of a positive integer n, where the number of times a particular colored part m may appear in a partition of n is equal to the sum of the powers of the divisors of m. An asymptotic formula is derived for the number of such partitions. We also derive an asymptotic formula for the number of partitions of n into c colors. In order to achieve the desired bounds on the minor arcs arising from the Hardy-Littlewood circle method, we generalize a bound on an exponential sum twisted by a generalized divisor function due to Motohashi.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.