weil representation
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2021 ◽  
Vol 193 (3) ◽  
pp. 863
Author(s):  
Zhang


2020 ◽  
pp. 1-36
Author(s):  
OLIVER STEIN

We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of $\operatorname{Sp}(n,\mathbb{Z})$ on $\mathbb{C}[(L^{\prime }/L)^{n}]$ . By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree $n$ , a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard $L$ -function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way.



2019 ◽  
Vol 22 (6) ◽  
pp. 975-999
Author(s):  
Moumita Shau ◽  
Fernando Szechtman

Abstract Let {\mathcal{O}} be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of {\mathcal{O}} by a nonzero power of its maximal ideal, and let {*} be the involution that A inherits from {\mathcal{O}} . We consider various unitary groups {\mathcal{U}_{m}(A)} of rank m over A, depending on the nature of {*} and the equivalence type of the underlying hermitian or skew hermitian form. Each group {\mathcal{U}_{m}(A)} gives rise to a Weil representation. In this paper, we give a Clifford theory description of all irreducible components of the Weil representation of {\mathcal{U}_{m}(A)} with respect to all of its abelian congruence subgroups and a third of its nonabelian congruence subgroups.



2019 ◽  
Vol 15 (02) ◽  
pp. 265-287 ◽  
Author(s):  
Brandon Williams

We study the (mock) Eisenstein series [Formula: see text] of weight [Formula: see text] for the Weil representation on an even lattice, defined as the result of Bruinier and Kuss’s coefficient formula for the Eisenstein series naively evaluated at [Formula: see text]. We describe the transformation law of [Formula: see text] in general. Most of this paper is dedicated to collecting examples where the coefficients of [Formula: see text] contain interesting arithmetic information. Finally, we make a few remarks about the case [Formula: see text].



2018 ◽  
Vol 193 ◽  
pp. 74-90 ◽  
Author(s):  
Markus Schwagenscheidt


2018 ◽  
Vol 47 (3) ◽  
pp. 605-650 ◽  
Author(s):  
Brandon Williams
Keyword(s):  




2017 ◽  
Vol 180 ◽  
pp. 474-497
Author(s):  
Luca Candelori ◽  
Cameron Franc ◽  
Gene S. Kopp


2017 ◽  
Vol 234 ◽  
pp. 139-169
Author(s):  
ERIC HOFMANN

For the modular variety attached to an arithmetic subgroup of an indefinite unitary group of signature $(1,n+1)$, with $n\geqslant 1$, we study Heegner divisors in the local Picard group over a boundary component of a compactification. For this purpose, we introduce local Borcherds products. We obtain a precise criterion for local Heegner divisors to be torsion elements in the Picard group, and further, as an application, we show that the obstructions to a local Heegner divisor being a torsion element can be described by certain spaces of vector-valued elliptic cusp forms, transforming under a Weil representation.



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