A new Ramanujan-type identity for L(2 k+ 1 , χ1)

Abstract

One of the celebrated formulas of Ramanujan is about odd zeta values, which has been studied by many mathematicians over the years. A notable extension was given by Grosswald in 1972. Following Ramanujan’s idea, we rediscovered a Ramanujan-type identity for ζ(2 k+ 1) that was first established by Malurkar and later by Berndt using different techniques. In the current paper, we extend the aforementioned identity of Malurkar and Berndt to derive a new Ramanujan-type identity for L(2 k+ 1 , χ1) , where χ1 is the principal character modulo prime p. In the process, we encounter a new family of Ramanujan-type polynomials. Furthermore, we establish a character analogue of Grosswald’s identity. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.