Eisenstein series for the Weil representation
نویسندگان
چکیده
منابع مشابه
A Simple Proof of Rationality of Siegel-weil Eisenstein Series
This short article is concerned with the arithmetic properties of the most degenerate holomorphic Eisenstein series on quasi-split 2n-dimensional unitary similitude groups GU(n, n) attached to totally imaginary quadratic extensions of totally real fields. This topic has been treated in detail in the literature, especially by Shimura. The general principle is that holomorphic Eisenstein series o...
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 کاملThe simplest Eisenstein series
We explain some essential aspects of the simplest Eisenstein series for SL2(Z) on the upper half-plane H. There are many different proofs of meromorphic continuation and functional equation of the simplest Eisenstein series for Γ = SL2(Z). We will follow [Godement 1966a] rewriting of a Poisson summation argument that appeared in [Rankin 1939], if not earlier. This argument is the most elementar...
متن کاملTheta Series Associated with the Schrödinger-weil Representation
In this paper, we define the Schrödinger-Weil representation for the Jacobi group and construct covariant maps for the Schrödinger-Weil representation. Using these covariant maps, we construct Jacobi forms with respect to an arithmetic subgroup of the Jacobi group.
متن کاملThe Weil Representation
This is my senior honors thesis done in my final year as an undergraduate at Stanford University, under the direction of Professor Akshay Venkatesh. We will construct the Weil representation of SL2(R) through a natural action of the Heisenberg group Heis(R) on the space of square-integrable complex-valued functions L 2(R), together with the celebrated Stone-von Neumann theorem of functional ana...
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: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.05.014