Lewis-Zagier Correspondence for higher order forms

نویسنده

  • Anton Deitmar
چکیده

The Lewis-Zagier correspondence, which attaches period functions to Maaß wave forms, is extended to wave forms of higher order, which are higher invariants of the Fuchsian group in question. The key ingredient is an identification of Higher order invariants with ordinary invariants of unipotent twists. This makes it possible to apply standard methods of automorphic forms to higher order forms.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A thermodynamic formalism approach to period functions for Maass forms and generalisations

In this paper we study one-parameter families of signed transfer operators P± q associated to the Farey map, as well as two-parameter families of operators for the Gauss map, obtained from the Farey map by inducing. We characterise all the analytic eigenfunctions of P± q with eigenvalue λ not embedded in the continuous spectrum, which for λ = 1 are the period functions for Maass forms studied b...

متن کامل

Period functions for Maass wave forms

Contents Introduction Chapter I. The period correspondence via L-series 1. The correspondences u ↔ Lε ↔ f ↔ ψ 2. Periodicity, L-series, and the three-term functional equation 3. Even and odd 4. Relations between Mellin transforms; proof of Theorem 1 Chapter II. The period correspondence via integral transforms 1. The integral representation of ψ in terms of u 2. The period function as the integ...

متن کامل

0 M ar 2 00 3 Transfer operators for Γ 0 ( n ) and the Hecke operators for the period functions of PSL ( 2 , Z ) 1

In this article we report on a surprising relation between the transfer operators for the congruence subgroups Γ0(n) and the Hecke operators on the space of period functions for the modular group PSL(2,Z). For this we study special eigenfunctions of the transfer operators with eigenvalues ∓1, which are also solutions of the Lewis equations for the groups Γ0(n) and which are determined by eigenf...

متن کامل

Stark–Heegner points and the Shimura correspondence

Let g = ∑ c(D) qD and f = ∑ an q n be modular forms of half-integral weight k + 1/2 and integral weight 2k respectively which are associated to each other under the ShimuraKohnen correspondence. For suitable fundamental discriminants D, a theorem of Waldspurger relates the coe cient c(D) to the central critical value L(f,D, k) of the Hecke L-series of f twisted by the quadratic Dirichlet charac...

متن کامل

Remarks on Modular Symbols for Maass Wave Forms

Abstract. In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the Boolean algebra generated by intervals with non–positive rational ends, with values in analytic functions (pseudo–measures in the sense of [MaMar2]). After explaining the basic issues and analogies in the extended Introduction, I construct modular symbols...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009