APPELL-LERCH SERIES VIEWED AS MOCK THETA FUNCTIONS

Changgui Zhang (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

The goal of this paper is to prove that the quotient of a first order Appell-Lerch series by a suitable theta-function can be written, near every given root of unity, as the sum of two functions, one of which has a finite limit and the other one has an asymptotic behavior like as one Jacobi's theta-function when q tends to this root. In order to simplify the exposition, we propose the definition of what we mean almost theta-type function, false theta-type function and mock theta-type function. The utilization of continued fractions and linear fractional transformations plays a central role in this paper.

Domaines: Mathématiques [math]

Changgui Zhang. APPELL-LERCH SERIES VIEWED AS MOCK THETA FUNCTIONS. 2015. ⟨hal-01230050⟩