Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2
نویسندگان
چکیده
منابع مشابه
Harmonic Maass Forms of Weight One
The object of this paper is to initiate a study of the Fourier coefficients of a weight one harmonic Maass form and relate them to the complex Galois representation associated to a weight one newform, which is the form’s image under a certain differential operator. In this paper, our focus will be on weight one dihedral newforms of prime level p ≡ 3 (mod 4). In this case we give properties of t...
متن کاملCoefficients of Harmonic Maass Forms
Harmonic Maass forms have recently been related to many different topics in number theory: Ramanujan’s mock theta functions, Dyson’s rank generating functions, Borcherds products, and central values and derivatives of quadratic twists of modular L-functions. Motivated by these connections, we obtain exact formulas for the coefficients of harmonic Maass forms of non-positive weight, and we obtai...
متن کاملDeformations of Maass forms
We describe numerical calculations which examine the PhillipsSarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface S under deformation of the surface. Our calculations indicate that if the Teichmüller space of S is not trivial, then each cusp form has a set of deformations under which either the cusp form remains a cusp form or else it dissol...
متن کاملq-series and weight 3/2 Maass forms
Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of t...
متن کاملAlgebraic Formulas for the Coefficients of Half-integral Weight Harmonic Weak Maass Forms
We prove that the coefficients of certain weight −1/2 harmonic Maass forms are “traces” of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight −2 harmonic weak Maass forms to spaces of weight −1/2 vectorvalued harmonic weak Maass forms on Mp2(Z), a result which is of independent interest. We then prove a general theorem which guarantees (...
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: Acta Arithmetica
سال: 2000
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-94-2-103-152