An identity for sums of polylogarithm functions

Abstract

We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to expanding moments of Satake parameters of holomorphic cuspidal newforms in terms of the moments of the corresponding Fourier coefficients, which has applications in analyzing lower order terms in the behavior of zeros of L-functions near the central point.

9 pages

References in corpus (4)

• 1- and 2-Level Densities for Rational Families of Elliptic Curves: Evidence for the Underlying Group Symmetries
• On the spacing distribution of the Riemann zeros: corrections to the asymptotic result
• Variation in the number of points on elliptic curves and applications to excess rank
• Constructing Elliptic Curves over $\mathbb{Q}(T)$ with Moderate Rank

Cited by in corpus (3)

• Effective equidistribution and the Sato-Tate law for families of elliptic curves
• Doubling coverings of algebraic hypersurfaces
• A combinatorial identity for studying Sato-Tate type problems