Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

DOI10.1007/S11139-013-9539-2zbMath1301.33026arXiv0909.3597OpenAlexW1977882410MaRDI QIDQ464428

Allal Ghanmi, Ahmed Intissar, Youssef Hantout

Publication date: 17 October 2014

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

Full work available at URL: https://arxiv.org/abs/0909.3597

zbMATH Keywords

Poincaré seriestheta functionsTaylor coefficientsHermite-Gauss seriesWeierstrass sigma-function

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Theta functions and abelian varieties (14K25) Theta series; Weil representation; theta correspondences (11F27) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Elliptic functions and integrals (33E05)

Related Items (2)

System of partial differential equations and analytical representations of the Weierstrass sigma function ⋮ Analytic and arithmetic properties of the \((\Gamma ,\chi )\)-automorphic reproducing kernel function and associated Hermite-Gauss series

Cites Work

• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• On a Hilbert space of analytic functions and an associated integral transform part I
• Bilinear operators and the power series for the Weierstrass sigma function
• On the dimension of the space of theta functions
• Landau automorphic functions on Cn of magnitude ν
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