Taylor coefficients of the Jacobi \(\theta_3(q)\) function

DOI10.1016/j.jnt.2020.03.002zbMath1456.11066OpenAlexW3023417005MaRDI QIDQ784722

Tanay Wakhare, Christophe Vignat

Publication date: 3 August 2020

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2020.03.002

zbMATH Keywords

elliptic functionsJacobi theta functiondiscrete Gaussian distribution

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27)

Related Items (1)

\(p\)-adic properties for Taylor coefficients of half-integral weight modular forms on \(\Gamma_1(4)\)

Uses Software

• Theta3Romik

Cites Work

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• The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004
• Sixteen Eisenstein series
• Une approche combinatoire des fonctions elliptiques de Jacobi
• On the combinatorics of cumulants
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
• The Taylor coefficients of the Jacobi theta constant \(\theta_3\)
• Elliptic and Modular Functions from Gauss to Dedekind to Hecke
• A Combinatorial Interpretation for the Schett Recurrence on the Jacobian Elliptic Functions
• Calculation of the Taylor Series Expansion Coefficients of the Jacobian Elliptic Function sn(x, k)
• Generalization of Certain Summations Due to Ramanujan

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