Hilbert modular forms of weight 1/2 and theta functions

نویسنده

  • SEVER ACHIMESCU
چکیده

Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result under certain mild restrictions on the level and character to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical difficulties which arise when we move out of Q.

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

The Eichler Commutation Relation for theta series with spherical harmonics

It is well known that classical theta series which are attached to positive definite rational quadratic forms yield elliptic modular forms, and linear combinations of theta series attached to lattices in a fixed genus can yield both cusp forms and Eisenstein series whose weight is one-half the rank of the quadratic form. In contrast, generalized theta series—those augmented with a spherical har...

متن کامل

Theta Functions of Indefinite Quadratic Forms over Real Number Fields

We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.

متن کامل

Theta functions of quadratic forms over imaginary quadratic fields

is a modular form of weight n/2 on Γ0(N), where N is the level of Q, i.e. NQ−1 is integral and NQ−1 has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly. Stark [8] gives a different proof by converting θ...

متن کامل

Theta Functionswith Harmonic Coe⁄cients over Number Fields

is a modular form of weight n=2þ n on G0ðN Þ, where G 1⁄4 SL2ðZÞ and N is the level of Q, i.e., NQ 1 is integral and NQ 1 has even diagonal entries. This was proved by Schoeneberg [13] for even n and by Pfetzer [9] for odd n. Shimura [14] generalizes their results for arbitrary n and also computes the theta multiplier explicitly. Andrianov and Maloletkin [1, 2] generalize (1) and define theta s...

متن کامل

On the Basis Problem for Siegel-hilbert Modular Forms

In this paper, we mainly announce the result: every Siegel-Hilbert cuspform of weight divisible by 4h and of square-free level relative to certain congruence subgroups is a linear combination of theta series. I N T R O D U C T I O N Theta series provides one of the two most explicit ways to construct holomorphic modular forms. The other way is by Eisenstein series. A virtue of theta series is t...

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 2008