Let E/F be a quadratic extension of number fields. For a cuspidal representation π of SL2(AE), we study in this paper the integral of functions in π on SL2(F)\SL2(AF). We characterize the nonvanishing of these integrals, called period integrals, in terms of π having a Whittaker model with respect to characters of E\AE which are trivial on AF . We show that the period integral in general is not ...

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions‎. ‎It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...

Introduction 2 1. Preliminaries on conformal algebras and modules 4 2. Basic definitions 9 3. Extensions and deformations 13 4. Homology 17 5. Exterior multiplication, contraction, and module structure 18 6. Cohomology of conformal algebras and their annihilation Lie algebras 19 6.1. Cohomology of the basic complex 19 6.2. Cohomology of the reduced complex 21 6.3. Cohomology of conformal algebr...

We obtain an asymptotic formula for a weighted sum over cuspidal eigenvalues in a specific region, for SL2 over a totally real number field F , with a discrete subgroup of Hecke type Γ0(I) for a non-zero ideal I in the ring of integers of F . The weights are products of Fourier coefficients. This implies in particular the existence of infinitely many cuspidal automorphic representations with mu...

The papers [Gálvez et al. 2000, Kokubu et al. 2003, Kokubu et al. 2005] gave a method of constructing flat surfaces in the three-dimesnional hyperbolic space. Such surfaces have generically singularities, since any closed nonsigular flat surface is isometric to a horosphere or a hyperbolic cylinder. In the paper [Sasaki et al. 2006], we defined a map, called the hyperbolic Schwarz map, from the...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

For an optimal elliptic curve E over Fq(t) of conductor p·∞, where p is prime, we show that E(F )tor is generated by the image of the cuspidal divisor group.

We establish a Springer theory for classical symmetric pairs. give an explicit description of character sheaves in this setting. In particular we determine the cuspidal sheaves.

Abstract It is known that irreducible cuspidal characters satisfy the preservation principle in Howe correspondences of finite reductive dual pairs. In this article, we generalize to any classical groups.