A note on vector-valued Eisenstein series of weight $3/2$
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 507-514
https://doi.org/10.4134/BKMS.b200375
Published online February 24, 2021
Printed March 31, 2021
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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