Hypergeometric functions over and traces of Frobenius for elliptic curves

Authors:
Rupam Barman and Gautam Kalita

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3403-3410

MSC (2010):
Primary 11T24, 11G20

Published electronically:
June 21, 2013

MathSciNet review:
3080163

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Abstract | References | Similar Articles | Additional Information

Abstract: We present explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of -hypergeometric functions over for and .

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Additional Information

**Rupam Barman**

Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India

Email:
rupamb@tezu.ernet.in

**Gautam Kalita**

Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India

Email:
gautamk@tezu.ernet.in

DOI:
https://doi.org/10.1090/S0002-9939-2013-11617-5

Keywords:
Gaussian hypergeometric series,
elliptic curves,
Frobenius endomorphisms

Received by editor(s):
August 19, 2011

Received by editor(s) in revised form:
December 21, 2011

Published electronically:
June 21, 2013

Additional Notes:
The first author thanks the Mathematical Institute, University of Heidelberg and Mathematics Center Heidelberg (MATCH), where the majority of this research was conducted. He is grateful to John H. Coates, R. Sujatha, Otmar Venjakob, and Anupam Saikia for their encouragement.

The second author was partially supported by an INSPIRE Fellowship of the Department of Science and Technology, Goverment of India.

Finally, the authors thank Ken Ono and the referee for helpful comments.

Communicated by:
Ken Ono

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.