On Period Relations for Automorphic L-functions II

Abstract

We study Hecke algebras for pairs $(\mathfrak{g},K)$ over arbitrary fields $E$ of characteristic $0$, define the Bernstein functor and give another definition of the Zuckerman functor over $E$. Building on this and the author's previous work on rational structures on automorphic representations, we show that hard duality remains valid over $E$ and apply this result to the study of rationality properties of Sun's cohomologically induced functionals. Our main application are period relations for the special values of standard $L$-functions of automorphic representations of $\mathrm{GL}(2n)$ admitting Shalika models.

updated references to "On Rational Structures on Automorphic Representations"

References in corpus (3)

• Notes on the arithmetic of Hilbert modular forms
• Period relations for automorphic induction and applications, I
• Eisenstein Cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions

Cited by in corpus (5)

• Dg analogues of the Zuckerman functors and the dual Zuckerman functors I
• $L$-functions of $\mathrm{GL}(2n):$ $p$-adic properties and non-vanishing of twists
• Flat Base Change Formulas for $(\mathfrak{g},K)$-modules over Noetherian rings
• Integral models of Harish-Chandra modules of the finite covering groups of PU(1,1)
• Special values of $L$-functions and the refined Gan-Gross-Prasad conjecture