Journal of the Ramanujan Mathematical Society
Volume 41, Issue 1, March 2026 pp. 53–60.
Special values of derivatives of certain L-functions
Authors:
Tapas Chatterjee and Sonika Dhillon
Author institution:Department of Mathematics, Indian Institute of Technology Ropar.
Summary:
In this paper we address the question of non-vanishing of L'(0, f) where f is an algebraic valued periodic
function. In 2011, Gun, Murty and Rath studied the nature of special values of the derivatives of even Dirichlet-type
functions and proved that it can be either zero or transcendental. Here for some special cases we characterize the set
of functions for which L'(0, f) is zero or transcendental. Using a theorem of Ramachandra about multiplicative independence
of cyclotomic units we also provide some non-trivial examples of functions where L'(0, f) is zero. Finally,
assuming Schanuel's conjecture we derive the algebraic independence of special values of derivatives of L-functions.
Contents
Full-Text PDF