L-series of Eisenstein series vanishing at critical values
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 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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Mathematical Identities
Analytic Number Theory Research
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publication date
- 10 February 2026
- Language
- EN