Eisenstein Series with Class Number Coefficients Constructed from the Weil Representation

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Date
2023-08-15
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Johns Hopkins University
Abstract
We generalize the work found in the paper [KY10] of Kudla and Yang to the case of Hilbert modular forms that come from the Weil representation associated to a 1-dimensional quadratic space. We also provide a computation of the level groups of certain forms produced this way. To achieve our results, we compute closed-form formulas for quadratic Gauss sums over local fields of characteristic 0. This includes the case of both odd and even residue characteristic.
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Keywords
Modular Forms, Hurwitz Class Numbers, Gauss Sums
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