Moments of elliptic integrals and critical \(L\)-values

DOI10.1007/s11139-014-9584-5zbMath1383.11048arXiv1303.2259OpenAlexW2066558222MaRDI QIDQ2345885

I. J. Zucker, James G. Wan, Mathew D. Rogers

Publication date: 21 May 2015

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2259

zbMATH Keywords

hypergeometric functionslattice sumsGamma functionscritical \(L\)-valuesmoments of elliptic integrals

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Other Dirichlet series and zeta functions (11M41) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic functions and integrals (33E05) Elliptic integrals as hypergeometric functions (33C75)

Related Items (18)

The arithmetic and topology of differential equations ⋮ Integrals of \(K\) and \(E\) from lattice sums ⋮ On the supercongruence conjectures of van Hamme ⋮ On a \(q\)-deformation of modular forms ⋮ A hypergeometric version of the modularity of rigid Calabi-Yau manifolds ⋮ Kontsevich-Zagier integrals for automorphic Green's functions. I ⋮ Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold ⋮ New Clebsch–Gordan‐type integrals involving threefold products of complete elliptic integrals ⋮ On a higher-order version of a formula due to Ramanujan ⋮ Legendre functions, spherical rotations, and multiple elliptic integrals ⋮ Hilbert transforms and sum rules of Bessel moments ⋮ On some integrals over the product of three Legendre functions ⋮ On Laporta's 4-loop sunrise formulae ⋮ Computing special \(L\)-values of certain modular forms with complex multiplication ⋮ ON BORWEIN’S CONJECTURES FOR PLANAR UNIFORM RANDOM WALKS ⋮ Moments in Pearson's four-step uniform random walk problem and other applications of very well-poised generalized hypergeometric series ⋮ On special values at integers of \(L\)-functions of Jacobi theta products of weight 3 ⋮ The special values of \(L\)-functions at \(s=1\) of theta products of weight 3

Cites Work

• Identities for the Ramanujan zeta function
• Legendre functions, spherical rotations, and multiple elliptic integrals
• Moments of products of elliptic integrals
• On the periods of modular forms
• On the Mahler Measure of 1+X+1/X+Y +1/Y
• Hypergeometric Formulas for Lattice Sums and Mahler Measures
• Some entries in Ramanujan's notebooks
• ON η3( aτ) η3( bτ) WITH a+ b=8
• The special values of the zeta functions associated with cusp forms
• The evaluation in terms of Γ-functions of the periods of elliptic curves admitting complex multiplication
• Three-Step and Four-Step Random Walk Integrals
• Multiplicative 𝜂-quotients
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