Hypergeometric functions over $\mathbb {F}_q$ and traces of Frobenius for elliptic curves
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- by Rupam Barman and Gautam Kalita PDF
- Proc. Amer. Math. Soc. 141 (2013), 3403-3410 Request permission
Abstract:
We present explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of ${_{2}}F_1$-hypergeometric functions over $\mathbb {F}_q$ for $q \equiv 1 ( \text {mod}~6)$ and $q \equiv 1 ( \text {mod}~4)$.References
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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
- MR Author ID: 981394
- Email: gautamk@tezu.ernet.in
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3403-3410
- MSC (2010): Primary 11T24, 11G20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11617-5
- MathSciNet review: 3080163