Periods of Hilbert modular forms, Kronecker series and cohomology
نویسندگان
چکیده
Generalizing a result of [24] , [8] about elliptic modular forms, we give closed formula for the sum all Hilbert Hecke eigenforms over totally real number field with strict class 1, multiplied by their period polynomials, as single product Kronecker series.
منابع مشابه
L - Functions of 2 X 2 Unitary Groups and Factorization of Periods of Hilbert Modular Forms
The object of this paper is to prove, under mild local hypotheses, a conjecture of Shimura on the factorization of Petersson norms of Hilbert modular forms. A special case of the conjecture is the following. Let E be a totally real field of degree dover Q, and let 1: = {ai' ... , ad} be the set of real embeddings of E. Let I be a Hilbert modular cusp form of weight (kl' ... , kd), where kl == k...
متن کاملNetworks via Hilbert Modular Forms
Ramanujan graphs, introduced by Lubotzky, Phillips and Sarnak, allow the design of efficient communication networks. In joint work with B. Jordan we gave a higher-dimensional generalization. Here we explain how one could use this generalization to construct efficient communication networks which allow for a number of verification protocols and for the distribution of information along several c...
متن کاملPeriods of Hilbert Modular Forms and Rational Points on Elliptic Curves
Let E be a modular elliptic curve over a totally real field. In [7, Chapter 8] the first author formulates a conjecture allowing the construction of canonical algebraic points on E by suitably integrating the associated Hilbert modular form. The main goal of the present paper is to obtain numerical evidence for this conjecture in the first case where it asserts something nontrivial, namely, whe...
متن کاملHilbert modular forms and the Ramanujan conjecture
Let F be a totally real field. In this paper we study the Ramanujan Conjecture for Hilbert modular forms and the Weight-Monodromy Conjecture for the Shimura varieties attached to quaternion algebras over F . As a consequence, we deduce, at all finite places of the field of definition, the full automorphic description conjectured by Langlands of the zeta functions of these varieties. Concerning ...
متن کاملHeegner points and Hilbert modular forms
(Here ΛE is a suitable period lattice commensurable with the Néron lattice of E.) The function Φ, which is transcendental as a function of τ , enjoys the following notable algebraicity property, a consequence of the theory of complex multiplication: Theorem HP: Let K ⊂ C be a quadratic imaginary extension of Q, and let K denote its maximal abelian extension. If τ belongs to H ∩ K, then Φ(τ) bel...
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: Advances in Mathematics
سال: 2021
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2021.107617