2022/01/25 by Nikolaos Diamantis, Larry Rolen, Diamantis, Nikolaos +1
Mathematics · #11F67 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2201.10193
openalex publication_date 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bruinier, Funke, and Imamoglu have proved a formula for what can philosophically be called the "central L-value" of the modular j-invariant. Previously, this had been heuristically suggested by Zagier. Here, we interpret this "L-value" as the value of an actual L-series, and extend it to all integral arguments and to a large class of harmonic Maass forms which includes all weakly holomorphic cusp forms. The context and relation to previously defined L-series for weakly holomorphic and harmonic Maass forms are discussed. These formulas suggest possible arithmetic or geometric meaning of L-values in these situations. The key ingredient of the proof is to apply a recent theory of Lee, Raji, and the authors to describe harmonic Maass L-functions using test functions.