In this paper we will prove bounds for the fourth power moment in the t aspect over a short interval of automorphic L-functions L(s, g) for GL(2) on the central critical line Re s = 1/2. Here g is a fixed holomorphic or Maass Hecke eigenform for the modular group SL2(Z), or in certain cases, for the Hecke congruence subgroup Γ0(N ) with N > 1. The short interval is from a large K to K + K103/13...

We prove explicit rationality-results for Asai- $L$-functions, $L^S(s,\Pi',{\rm As}^\pm)$, and Rankin-Selberg $L^S(s,\Pi\times\Pi')$, over arbitrary CM-fields $F$, relating critical values to powers of $(2\pi i)$. Besides determining the contribution archimedean zeta-integrals our formulas as concrete i)$, it is one advantages approach, that applies very general non-cuspidal isobaric automorphi...

Abstract In this paper, we prove the Gan-Gross-Prasad conjecture and Ichino-Ikeda for unitary groups $U_{n}\times U_{n+1}$ U n × + 1 in all endoscopic cases. Our main technical innovation is compu...

Introduction 2 1. Preliminaries 6 1.1. Algebraic modular forms 6 1.2. Modular forms over C 9 1.3. p-adic modular forms 11 1.4. Elliptic curves with complex multiplication 12 1.5. Values of modular forms at CM points 14 2. Generalised Heegner cycles 15 2.1. Kuga-Sato varieties 15 2.2. The variety Xr and its cohomology 18 2.3. Definition of the cycles 19 2.4. Relation with Heegner cycles and L-se...

Let F be a number field and K a quadratic algebra over F , i.e., either F × F or a quadratic field extension of F . Denote by G the F -group defined by GL(2)/K. Then, given any cuspidal automorphic representation π of G(AF ), one has (cf. [8], [9]) a transfer to an isobaric automorphic representation Π of GL4(AF ) corresponding to the L-homomorphism LG → LGL(4). Usually, Π is called the Rankin-...

The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class Rankin-Selberg tensor products. Although the conjecture is not proved in full generality, there been considerable progress, especially $L$-values form $L(1/2,BC(\pi) \times BC(\pi'))$, where $\pi$ $\pi'$ are cohomological automorphic repres...

α∈R (∣∣〈ρk, α∨〉+ kα + 1 2kα/2∣∣)! (∣∣〈ρk, α∨〉+ 1 2kα/2∣∣)! • Also in 1982, A. Koranyi uses the Selberg formula to compute the volumes of bounded symmetric domains. • In 1987, K. Aomoto studies a slight generalization of the Selberg integral arising from work on Fock space representations of the Virasoro algebra. Here a connection with hypergeometric functions, specifically Jacobi polynomials is...