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arXiv · 2401.08230

L-series of Eisenstein series vanishing at critical values

Johann Franke
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Abstract

Using the relations between rational functions and Eisenstein series, as well as the inferences for cotangent sums and period polynomials, we work out a precise description for Eisenstein series whose $L$-series vanish at certain critical values. This is possible for small weights compared to the level of the Eisenstein series. For large weights we give a partial result and determine subspaces with simultaneous vanishing properties.

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Johann Franke. 2024-01-16. L-series of Eisenstein series vanishing at critical values. https://arxiv.org/abs/2401.08230

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