Two identities relating Eisenstein series on classical groups
نویسندگان
چکیده
In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well double covers of symplectic groups. The first identity can be viewed an extension the doubling construction introduced in [CFGK19] . second is a generalization descent studied [GRS11]
منابع مشابه
Transition: Eisenstein series on adele groups
[1] Despite contrary assertions in the literature, rewriting Eisenstein series, as opposed to more general automorphic forms, on adele groups does not use Strong Approximation. Strong Approximation does make precise the relation between general automorphic forms on adele groups and automorphic forms on SL2 and even on SLn, but rewriting these Eisenstein series does not need this comparison. Ind...
متن کاملComputations of Eisenstein series on Fuchsian groups
We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z; s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real-valued rotation of E(z; s) as Re s = 1/2, Im s → ∞ and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z; s) when ...
متن کاملEisenstein Series on Affine Kac-moody Groups over Function Fields
In his pioneering work, H. Garland constructed Eisenstein series on affine Kac-Moody groups over the field of real numbers. He established the almost everywhere convergence of these series, obtained a formula for their constant terms, and proved a functional equation for the constant terms. In his subsequent paper, the convergence of the Eisenstein series was obtained. In this paper, we define ...
متن کاملOn Zeros of Eisenstein Series for Genus Zero Fuchsian Groups
Let Γ ≤ SL2(R) be a genus zero Fuchsian group of the first kind with ∞ as a cusp, and let E 2k be the holomorphic Eisenstein series of weight 2k on Γ that is nonvanishing at ∞ and vanishes at all the other cusps (provided that such an Eisenstein series exists). Under certain assumptions on Γ, and on a choice of a fundamental domain F , we prove that all but possibly c(Γ,F) of the non-trivial ze...
متن کاملTransition exercise on Eisenstein series
[1] Despite occasional contrary assertions in the literature, rewriting Eisenstein series, as opposed to more general automorphic forms, to make sense on adele groups is not about Strong Approximation. Strong Approximation does make precise the relation between general automorphic forms on adele groups and automorphic forms on SLn, but rewriting these Eisenstein series does not need this compar...
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: 2021
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2020.11.001