Derivatives of L-functions

Abstract

In this paper, we investigate the derivatives of L-functions, in particular, the Riemann zeta function, the Hasse-Weil L-function, the Rankin L-function and the Artin L-function, and survey the relations between the derivatives of L-functions and the geometry and arithmetic of the associated Shimura varieties.

53 pages

References in corpus (3)

• Heegner divisors, $L$-functions and harmonic weak Maass forms
• Height pairings on orthogonal Shimura varieties
• The Birch-Swinnerton-Dyer Conjecture