Computing Hecke Operators on Bianchi Forms

نویسنده

  • DAN YASAKI
چکیده

Bianchi forms are generalizations of classical modular forms. The arithmetic significance of these forms is revealed through the system eigenvalues determined by a family of linear operators known as Hecke operators.

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 Hardness of Computing an Eigenform Eric Bach and Denis Charles

The Fourier coefficients of modular forms encode very interesting arithmetic data. For example, divisor sums, partition numbers, trace of Frobenius of the reduction modulo primes of an elliptic curve over Q, and more generally, trace of Frobenius of many Galois representations of dimension 2 over finite fields (this being a conjecture of Serre) are all known to be, or conjectured to be, Fourier...

متن کامل

The Hecke algebra action on Morava E-theory of height 2

Given a one-dimensional formal group of height 2, let E be the Morava E theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an algebra of Hecke operators acting on E -cohomology. This leads to a vanishing result for Rezk’s logarithmic cohomology operation on the units of E . It identif...

متن کامل

The Weil Representation and Hecke Operators for Vector Valued Modular Forms

We define Hecke operators on vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular forms.

متن کامل

Hecke Operators for Weakly Holomorphic Modular Forms and Supersingular Congruences

We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.

متن کامل

Explicit Matrices for Hecke Operators on Siegel Modular Forms

We present an explicit set of matrices giving the action of the Hecke operators T (p), Tj(p ) on Siegel modular forms. Introduction It is well-known that the space of elliptic modular forms of weight k has a basis of simultaneous eigenforms for the Hecke operators, and the Fourier coefficients of an eigenform (and hence the eigenform) are completely determined by its eigenvalues and first Fouri...

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