Published on:

2 October 2023

Primary Category:

Number Theory

Paper Authors:

Joshua Drewitt,

Joshua Pimm

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Introduces L-series for real-analytic modular forms of higher level Γ0(N)

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Proves a functional equation and converse theorem for the L-series

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Gives examples like Eisenstein series and length-one iterated integrals

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Focuses on L-series for Brown's MI!1 modular iterated integrals

L-series of real-analytic modular forms

This paper introduces an L-series associated to real-analytic modular forms, which transform with weight (r,s) under the congruence subgroup Γ0(N). These L-series satisfy a functional equation and converse theorem. The paper discusses examples of such forms, including real analytic Eisenstein series and modular iterated integrals of higher level. It focuses on the L-series for a class of forms including Francis Brown's length-one modular iterated integrals MI!1.

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