Title of article :
Generalizations of Mock Theta Functions and Appell–Lerch Sums
Author/Authors :
Cui ، Su-Ping Department of Mathematics - School of Mathematics and Statistics - Qinghai Normal University , S.S. Gu ، Nancy Department of Mathematics - Center for Combinatorics - Nankai University , Tang ، Dazhao Department of Mathematics - School of Mathematical Sciences - Chongqing Normal University
Abstract :
Ramanujan named and first studied mock theta functions which can be represented by Eulerian forms, Appell–Lerch sums, Hecke-type double sums, and Fourier coefficients of meromorphic Jacobi forms. In this paper, we investigate some generalizations of mock theta functions and express them in terms of Appell–Lerch sums. For instance, one result proved in the present paper is that for any positive integer r , |q| 1, and x, so that no denominators vanish.
Keywords :
Mock theta functions , Universal mock theta functions , Appell–Lerch sums ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
