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Title: | Hypergeometric functions and algebraic curves ye = xd + ax + b |
Authors: | Kewat, Pramod Kumar |
Issue Date: | 2019 |
Publisher: | Journal of the Ramanujan Mathematical Society |
Abstract: | Let q be a prime power and IF q be a finite field with q elements. Let e and d be positive integers. In this paper, for d 2: 2 and q = l(mod ed(d - 1)), we calculate the number of points on an algebraic curve Ee,d : ye = xd + ax + b over a finite field IFq in terms of dFd-1 Gaussian hypergeometric series with multiplicative characters of orders d and e(d - 1 ), and in terms of d-1 Fd-2 Gaussian hypergeometric series with multiplicative characters of orders ed(d - 1) and e(d - 1). This helps us to express the trace of Frobenius endomorphism of an algebraic curve Ee,d over a finite field IF q in terms of above hypergeometric series. As applications, we obtain some transformations and special values of 2F1 hypergeometric series. |
URI: | http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/6372 |
Appears in Collections: | Articles to be qced |
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