Year: 2026
Type: preprint
Abstract: We derive a recurrence for logarithmically weighted Möbius sums by combining Möbius inversion with the Euler-Maclaurin summation formula. Consequently, starting from estimates of orders zero, one and two, we obtain polynomial approximations for these sums for every nonnegative integer exponent of $\log$. We then extend these estimates to sums with coprimality conditions via a convolution identity and to sums weighted by the reciprocal of the sum-of-divisors function. We also study the nonnegativity of the latter sums for every positive integer logarithmic order, establishing that they never change sign.
Source: arXiv (Cornell University)
Author: Alterman, Sebastian Zuniga
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221786811