Convolution Operators on Holomorphic Dirichlet Series
نویسندگان
چکیده
منابع مشابه
Special values of shifted convolution Dirichlet series
In a recent important paper, Hoffstein and Hulse [14] generalized the notion of Rankin-Selberg convolution L-functions by defining shifted convolution L-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.
متن کاملOn Non-Vanishing of Convolution of Dirichlet Series
We study the non-vanishing on the line Re(s) = 1 of the convolution series associated to two Dirichlet series in a certain class of Dirichlet series. The non-vanishing of various L-functions on the line Re(s) = 1 will be simple corollaries of our general theorems. Let f(z) = ∑∞ n=1 âf (n)e 2πinz and g(z) = ∑∞ n=1 âg(n)e 2πinz be cusp forms of weight k and level N with trivial character. Let Lf ...
متن کاملp-ADIC PROPERTIES OF MODULAR SHIFTED CONVOLUTION DIRICHLET SERIES
Ho stein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms f1 and f2. The second two authors investigated certain special values of symmetrized sums of such functions, numbers which are generally expected to be mysterious transcendental numbers. They proved that the generating functions of these values in the h-aspect are linear combinat...
متن کاملAsymptotic bounds for special values of shifted convolution Dirichlet series
In [15], Hoffstein and Hulse defined the shifted convolution series of two cusp forms by “shifting” the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of certain values of these series and prove a polynomial bound as h → ∞. Our method relies on a result of Mertens and Ono [22], who showed that these values ...
متن کاملOn Kubota’s Dirichlet Series
Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [2]. Closely related results are in Eckhardt and Pat...
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: Tokyo Journal of Mathematics
سال: 1997
ISSN: 0387-3870
DOI: 10.3836/tjm/1270042112