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PARTIAL INDEFINITE THETA IDENTITIES

Part of: Basic hypergeometric functions Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  19 September 2016

BYUNGCHAN KIM  and
JEREMY LOVEJOY
BYUNGCHAN KIM
Affiliation:
School of Liberal Arts, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Korea email bkim4@seoultech.ac.kr
JEREMY LOVEJOY*
Affiliation:
CNRS, LIAFA, Université Denis Diderot – Paris 7, Case 7014, 75205 Paris Cedex 13, France email lovejoy@math.cnrs.fr
*
✉ lovejoy@math.cnrs.fr
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Abstract

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Using a result of Warnaar, we prove a number of single- and multi-sum identities in the spirit of Ramanujan’s partial theta identities, but with partial indefinite binary theta functions in the role of partial theta functions. We also calculate the corresponding residual identities and use a result of Ji and Zhao to recast our identities in terms of indefinite ternary theta functions.

Keywords

partial theta functionsindefinite theta functionspartial indefinite theta functionsBailey pairs

MSC classification

Primary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Secondary: 11F27: Theta series; Weil representation; theta correspondences 11F37: Forms of half-integer weight; nonholomorphic modular forms

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 2 , April 2017 , pp. 255 - 289
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

This research was supported by the International Research & Development Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) of Korea (NRF-2014K1A3A1A21000358), and the STAR program number 32142ZM.

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