منابع مشابه
Modular Forms of Weight One
The decomposition into an Euler product and the functional equation of the Dirichlet series associated by Hecke to modular forms of weight one suggests that these correspond to Artin L-functions of degree 2 over Q, otherwise known as Galois representations Gal(Q/Q)→ GL2(C). It is this correspondence, conjectured by Langlands, which we establish here. The first three sections are preliminary. Th...
متن کاملMock-modular Forms of Weight One
The object of this paper is to initiate a study of the Fourier coefficients of a weight one mock-modular form and relate them to the complex Galois representations associated to the form’s shadow, which is a weight one newform. 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 the Fourier coefficients themselves tha...
متن کاملLevel-one elliptic modular forms
[1] Traditional terminology is that f → f |2kγ is the slash operator, although this name fails to suggest any meaning other than reference to the notation itself. In fact, obviously f(z)→ f(γz)(cz + d)−2k is a left translation operator, albeit complicated by the automorphy factor. That is, this is a right action of SL2(Z) on functions on H, while the group action of SL2(Z) on H is written on th...
متن کاملCoefficients of Half-integral Weight Modular Forms
In this paper we study the distribution of the coefficients a(n) of half integral weight modular forms modulo odd integers M . As a consequence we obtain improvements of indivisibility results for the central critical values of quadratic twists of L-functions associated with integral weight newforms established in [O-S]. Moreover, we find a simple criterion for proving cases of Newman’s conject...
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: Journal of Number Theory
سال: 1997
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2185