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arXiv · 1706.03738

Vector-valued Eisenstein series of small weight

Brandon Williams
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Abstract

We study the (mock) Eisenstein series $E_k$ of weight $k \in \{1,3/2,2\}$ 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 $k$. We describe the transformation law of $E_k$ in general. Most of this note is dedicated to collecting examples where the coefficients of $E_k$ contain interesting arithmetic information. Finally we make a few remarks about the case $k=1/2$.

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Brandon Williams. 2017-10-19. Vector-valued Eisenstein series of small weight. https://doi.org/10.1142/s1793042119500118

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