Limit values of Eisenstein series and multiple cotangent functions
نویسندگان
چکیده
منابع مشابه
Values of symmetric cube L-functions and Fourier coefficients of Siegel Eisenstein series of degree-3
We obtain formulas for certain weighted sums of values of the symmetric square and triple product L-functions. As a consequence, we get exact values at the right critical point for the symmetric square and symmetric cube L-functions attached to certain cuspforms. We also give applications to Fourier coefficients of modular forms.
متن کاملWeyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
If F is a local field containing the group μn of n-th roots of unity, and if G is a split semisimple simply connected algebraic group, then Matsumoto [27] defined an n-fold covering group of G(F ), that is, a central extension of G(F ) by μn. Similarly if F is a global field with adele ring AF containing μn there is a cover G̃(AF ) of G(AF ) that splits over G(F ). The construction is built on i...
متن کاملIntegrals of Eisenstein Series and Derivatives of L-functions
In his lost notebook, Ramanujan recorded a formula relating a “character analogue” of the Dedekind eta-function, the integral of a quotient of eta-functions, and the value of a Dirichlet Lfunction at s = 2. Here we derive an infinite family of formulas which includes Ramanujan’s original formula as a special case. Our results depend on a representation of values of the derivatives of Dirichlet ...
متن کاملEisenstein Series*
group GC defined over Q whose connected component G 0 Q has no rational character. It is also necessary to suppose that the centralizer of a maximal Q split torus of G0C meets every component of GC. The reduction theory of Borel applies, with trivial modifications, to G; it will be convenient to assume that Γ has a fundamental set with only one cusp. Fix a minimal parabolic subgroup P 0 C defin...
متن کاملConvolution Dirichlet Series and a Kronecker Limit Formula for Second-order Eisenstein Series
In this article we derive analytic and Fourier aspects of a Kronecker limit formula for second-order Eisenstein series. Let Γ be any Fuchsian group of the first kind which acts on the hyperbolic upper half-space H such that the quotient Γ\H has finite volume yet is non-compact. Associated to each cusp of Γ\H, there is a classically studied first-order non-holomorphic Eisenstein series E(s, z) w...
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: 2008
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2007.06.003