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L-series of Eisenstein series vanishing at critical values (2401.08230v2)
Published 16 Jan 2024 in math.NT
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.