Error functions, Mordell integrals and an integral analogue of a partial theta function

DOI10.4064/aa8207-5-2016zbMath1393.11058arXiv1605.08904OpenAlexW2963744698MaRDI QIDQ2957226

Alexandru Zaharescu, Atul Dixit, Arindam Roy

Publication date: 25 January 2017

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08904

zbMATH Keywords

Riemann zeta functionhypergeometric functionsasymptotic expansionsDirichlet \(L\)-functionpartial theta functionRamanujan's lost notebookMordell integrals

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Asymptotic expansions of solutions to ordinary differential equations (34E05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (3)

Superimposing theta structure on a generalized modular relation ⋮ Koshliakov zeta functions I: modular relations ⋮ A generalization of the Riemann-Siegel formula

Uses Software

• DLMF

Cites Work

• Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
• Character analogues of theorems of Ramanujan, Koshliakov and Guinand
• A nearly-optimal method to compute the truncated theta function, its derivatives, and integrals
• Fast methods to compute the Riemann zeta function
• The Mordell integral, quantum modular forms, and mock Jacobi forms
• Riesz-type criteria and theta transformation analogues
• Ramanujan's ``lost notebook. I: Partial Theta-functions
• Some elegant approximations and asymptotic formulas of Ramanujan
• Analogues of the general theta transformation formula
• An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook
• Computing the truncated theta function via Mordell integral
• Ramanujan's Lost Notebook
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