Formulas for some exponential and trigonometric character sums

Abstract: We express three different, yet related, character sums by generalized Bernoulli numbers. Two of these sums are generalizations of sums introduced and studied by Berndt and Arakawa-Ibukiyama-Kaneko in the context of the theory of modular forms. A third sum generalizes a sum already studied by Ramanujan in the context of theta function identities. Our methods are elementary, relying on basic facts from algebra and number theory.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

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