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- W4382603023 abstract "In this paper, we characterize the vanishing of twisted central $L$-values attached to newforms of square-free level in terms of so-called local polynomials and the action of finitely many Hecke operators thereon. Such polynomials are the ``local part'' of certain locally harmonic Maass forms constructed by Bringmann, Kane and Kohnen, and are explicitly computable. We provide numerical examples in weight $4$ and levels $7$, $15$, $22$, and the necessary code behind. Furthermore, we connect local polynomials to even period polynomials of newforms as well as to Rankin--Cohen brackets of an Eisenstein series and a theta function. Lastly, we generalize a result of Wong to link a natural additive constant inside these local polynomials to Fourier coefficients of Cohen--Eisenstein series." @default.
- W4382603023 created "2023-06-30" @default.
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- W4382603023 date "2023-06-27" @default.
- W4382603023 modified "2023-09-27" @default.
- W4382603023 title "Central $L$-values of newforms and local polynomials" @default.
- W4382603023 doi "https://doi.org/10.48550/arxiv.2306.15519" @default.
- W4382603023 hasPublicationYear "2023" @default.
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