The Kohnen-Zagier formula for Maass forms for $\Gamma_0(4)$
Nickolas Andersen
TL;DR
This paper extends a known formula to establish the Kohnen-Zagier formula specifically for Maass forms on the modular group , providing new insights into their spectral properties and Fourier coefficients.
Contribution
The paper generalizes previous formulas to derive the Kohnen-Zagier formula for Maass forms on , expanding the understanding of automorphic forms for this subgroup.
Findings
Established the Kohnen-Zagier formula for Maass forms
Extended the Duke-Imamoglu-T4 formula to new settings
Provided new relations between Fourier coefficients and L-values
Abstract
We extend a formula of Duke, Imam\=oglu, and T\'oth (which itself is a generalization of the Katok-Sarnak formula) to prove the Kohnen-Zagier formula for Maass forms for .
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Analytic Number Theory Research