The Completed L-function attached to the Weight 2 Polar Harmonic Maass Form H_N,z^*(τ)

2022/01/10 by Kush Singhal, Singhal, Kush
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2201.03146

Abstract

In this paper, we study the Mellin transform of the weight 2 level N polar harmonic Maass form H_N,z^*(τ), and analyze this (generalized) L-function as Im(z)→ ∞. On the way, we also calculate the Fourier expansion of H_N,z^*(τ) at arbitrary cusps of Γ₀(N), and we give a functional equation and factorization into local factors of the L-function for the weight 2 level N Eisenstein series at the cusps i∞ and 0.

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