Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2

CRITICAL VALUES OF RANKIN–SELBERG L-FUNCTIONS FOR GLn ×GLn−1 AND THE SYMMETRIC CUBE L-FUNCTIONS FOR GL2

In a previous article [35] an algebraicity result for the central critical value for L-functions for GLn × GLn−1 over Q was proved assuming the validity of a nonvanishing hypothesis involving archimedean integrals. The purpose of this article is to generalize [35, Thm. 1.1] for all critical values for L-functions for GLn×GLn−1 over any number field F while using the period relations of [37] and...

DERIVATIVES AND L-FUNCTIONS FOR GLn

Introduction to zeta integrals and L-functions for GLn

All known ways to analytically continue automorphic L-functions involve integral representations using the corresponding automorphic forms. The simplest cases, extending Hecke’s treatment of GL2, need no further analytic devices and very little manipulation beyond Fourier-Whittaker expansions. [1] Poisson summation is a sufficient device for several accessible classes of examples, as in Riemann...

Critical Values of Symmetric Power L-functions

We consider the critical values of symmetric power L-functions attached to elliptic curves over Q. We show how to calculate a canonical Deligne period, and in several numerical examples, especially for sixth and tenth powers, we examine the factorisation of the rational number apparently obtained when one divides the critical value by the canonical period. This seems to provide some support for...

Noncommutative Symmetric Functions V: a degenerate Version of UQ(Gln)

We interpret quasi-symmetric functions and noncommutative symmetric functions as characters of a degenerate quantum group obtained by putting q = 0 in a variant of Uq(glN).