2000 character limit reached
Sums of powers of binomials, their Apéry limits, and Franel's suspicions (2112.09576v2)
Published 17 Dec 2021 in math.NT, math.CA, and math.CO
Abstract: We explicitly determine the Ap\'ery limits for the sums of powers of binomial coefficients. As an application, we prove a weak version of Franel's conjecture on the order of the recurrences for these sequences. Namely, we prove the conjectured minimal order under the assumption that such a recurrence can be obtained via creative telescoping.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.