Taylor coefficients of the Jacobi θ3(q) function
| Autor: | Christophe Vignat, Tanay Wakhare |
|---|---|
| Přispěvatelé: | Department of Mathematics, University of Maryland, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Q-function 010102 general mathematics Theta function Taylor coefficients 01 natural sciences [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010101 applied mathematics 0101 mathematics Cumulant Random variable ComputingMilieux_MISCELLANEOUS Mathematics Variable (mathematics) |
| Zdroj: | Journal of Number Theory Journal of Number Theory, Elsevier, 2020, 216, pp.280-306. ⟨10.1016/j.jnt.2020.03.002⟩ |
| ISSN: | 0022-314X 1096-1658 |
| DOI: | 10.1016/j.jnt.2020.03.002 |
| Popis: | We extend some results recently obtained by Dan Romik [14] about the Taylor coefficients of the theta function θ 3 ( e − π ) to the case θ 3 ( q ) of a real valued variable 0 q 1 . These results are obtained by carefully studying the properties of the cumulants associated to a Jacobi θ 3 (or discrete normal) distributed random variable. This article also states some integrality conjectures about rational sequences that generalize the one studied by Romik. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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