Bulletin of the
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Bull. Korean Math. Soc. 2021; 58(2): 507-514

Online first article February 24, 2021      Printed March 31, 2021

https://doi.org/10.4134/BKMS.b200375

Copyright © The Korean Mathematical Society.

A note on vector-valued Eisenstein series of weight $3/2$

Ran Xiong

East China Normal University

Abstract

Vector-valued Eisenstein series of weight $3/2$ are often not holomorphic. In this paper we prove that, for an even lattice $\lat L$, if there exists an odd prime $p$ such that $\lat L$ is local $p$-maximal and the determinant of $\lat L$ is divisible by $p^{2}$, then the Eisenstein series of weight $3/2$ attached to the discriminant form of $\lat L$ is holomorphic.

Keywords: Vector valued Eisenstein series, Weil representation

MSC numbers: 11E41, 11F37, 11F30

Supported by: The author is financial supported by the Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice

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