Linear relations between L-values of newforms and moments of elliptic K integral

2025/09/24 by Au, Kam Cheong
#11F11 #11F67 #33C75 (Primary) 33C20 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.19960

Abstract

By systematically translating certain integrals involving moments of the elliptic integral into L-values of modular forms on Γ₁(4), Γ(4) and Γ₁(8), and then utilizing relations among the critical L-values of cuspidal newforms, we obtain a dimension formula for the space spanned by these integrals.

Citations

• The Explicit Hypergeometric-Modularity Method I
• D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods
• A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series
• On the interplay between hypergeometric series, Fourier-Legendre\n expansions and Euler sums
• Integrals of K and E from Lattice Sums
• Multiple Modular Values and the relative completion of the fundamental group of M_1,1
• Moments of elliptic integrals and critical L-values
• Moments of Products of Elliptic Integrals

Related

• Moments of elliptic integrals and critical L-values
• On the non-vanishing of modular L-values and fourier coefficients of cusp forms
• The shifted fourth moment of modular form L-functions in the weight aspect
• Fourier coefficients and cuspidality of modular forms: a new approach
• L-values of harmonic Maass forms