Some restricted sum formulas for double zeta values
Tomoya Machide
TL;DR
This paper derives new restricted sum formulas for double zeta values under specific congruence conditions and connects these to Ramanujan's identities involving Bernoulli numbers.
Contribution
It introduces novel restricted sum formulas for double zeta values and links them to classical identities by Ramanujan, expanding understanding of these special functions.
Findings
Derived sum formulas for double zeta values with congruence restrictions
Connected sum formulas to Ramanujan's identities involving Bernoulli numbers
Provided applications demonstrating the formulas' relevance
Abstract
We give some restricted sum formulas for double zeta values whose arguments satisfy certain congruence conditions modulo 2 or 6, and also give an application to identities showed by Ramanujan for sums of products of Bernoulli numbers with a gap of 6.
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