Real-analytic modular forms for Γ₀(N) and their L-series

2023/10/02 by Drewitt, Joshua, Pimm, Joshua
#11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.01127

Abstract

We introduce an L-series associated to real-analytic modular forms which transform with weight (r,s)∈ℤ² under Γ₀(N). These L-series satisfy a functional equation and converse theorem. We also discuss examples of such forms, including real analytic Eisenstein series and modular iterated integrals of higher level. We focus on the L-series for a class of forms including Francis Brown's length-one modular iterated integrals MI^!₁.

Related

• Period functions associated to real-analytic modular forms
• A class of non-holomorphic modular forms II : equivariant iterated\n Eisenstein integrals
• A class of non-holomorphic modular forms III: real analytic cusp forms\n for \SL₂(\ℤ)
• Petersson scalar products and L-functions arising from modular forms
• Eisenstein series identities based on partial fraction decomposition