منابع مشابه
Geometric Waldspurger periods
1.0 This paper, which is a sequel to [6], is a step towards a geometric version of the Howe correspondence (an analogue of the theta-lifting in the framework of the geometric Langlands program). We consider only the (unramified) dual reductive pair (H = GO2m, G = GSp2n) over a smooth projective connected curve X. Let BunG (resp., BunH) denote the stack of Gtorsors (resp., H-torsors) on X. Using...
متن کاملToroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series
The space of toroidal automorphic forms was introduced by Zagier in the 1970s: a GL2-automorphic form is toroidal if it has vanishing constant Fourier coefficients along all embedded non-split tori. The interest in this space stems (amongst others) from the fact that an Eisenstein series of weight s is toroidal for a given torus precisely if s is a non-trivial zero of the zeta function of the q...
متن کاملA p-ADIC WALDSPURGER FORMULA
In this article, we study p-adic torus periods for certain p-adic valued functions on Shimura curves coming from classical origin. We prove a p-adic Waldspurger formula for these periods, as a generalization of the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we construct a new anti-cyclotomic p-adic L-function of Rankin– Selberg type. At a character of positive w...
متن کاملON p-ADIC WALDSPURGER FORMULA
conjugation, c, 5anti-cyclotomic p-adic L-function, L (π), 6Atkin–Serre operator, Θord, 13 canonical pairing, ( ,)A, 23convergent modular form, M(m,K), 14admissible, 15of finite tame level, M[ (m,K), 14stable, M[ (m,K)♥, 14universal, 15 distribution algebraA-related, D(A,K), 25ω-related, D(ω,K), 25π-related, D(π), 4 global Lubin–Tate different...
متن کاملArithmetic Properties of the Shimura-shintani-waldspurger Correspondence
We prove that the theta correspondence for the dual pair (S̃L2, PB×), for B an indefinite quaternion algebra over Q, preserves rationality and p-integrality in both directions. As a consequence, we deduce the rationality of certain period ratios of modular forms and even p-integrality of these ratios under the assumption that p does not divide a certain L-value. The rationality is applied to giv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2008
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x07003156