Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

DOI10.1007/s11139-011-9351-9zbMath1290.11112arXiv1108.4980OpenAlexW2137376128MaRDI QIDQ1927665

Bruce C. Berndt, Mathew D. Rogers, George L. jun. Lamb

Publication date: 2 January 2013

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

Full work available at URL: https://arxiv.org/abs/1108.4980

zbMATH Keywords

Jacobian elliptic functionhypergeometric functionsingular moduliRogers-Ramanujan continued fractionRamanujan's theta functionclass invariantcubic continued fractiontwo-dimensional lattice sum

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Theta series; Weil representation; theta correspondences (11F27) Continued fractions (11A55) Trigonometric and exponential sums (general theory) (11L03) Elliptic functions and integrals (33E05)

Related Items (4)

A summation due to Ramanujan revisited ⋮ The evaluation of two-dimensional lattice sums via Ramanujan's theta functions ⋮ Compressed lattice sums arising from the Poisson equation ⋮ Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

Cites Work

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• Hypergeometric Formulas for Lattice Sums and Mahler Measures
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• Convergence of lattice sums and Madelung’s constant
• Madelung constants and lattice sums for hexagonal crystals
• New Representations for the Madelung Constant
• FromL-series of elliptic curves to Mahler measures

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