Please use this identifier to cite or link to this item:
https://gnanaganga.inflibnet.ac.in:8443/jspui/handle/123456789/6309
Title: | Hyperelliptic Curves Over and 120125Q and Gaussian Hypergeometric Series |
Authors: | Rupam Barman Gautam Kalita |
Issue Date: | 2015 |
Publisher: | Journal of the Ramanujan Mathematical Society |
Abstract: | Let da��2 be an integer. Denote by Ed and E'd the hyper-elliptic curves over 𝔽q given by Ed- y2 = xd + ax + b and E'd- y2 = xd + axda��1 + b, respectively. We explicitly find the number of 𝔽q-points on Ed and E'd in terms of special values of d Fd-1 and d-1Fd-2 Gaussian hypergeometric series with characters of orders d-1, d, 2(d-1), 2d, and 2d(d-1) as parameters. This gives a solution to a problem posed by Ken Ono [17, p. 204] on special values of n+1Fn Gaussian hypergeometric series for n>2. We also show that the results of Lennon [14] and the authors [4] on trace of Frobenius of elliptic curves follow from the main results. |
URI: | http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/6309 |
Appears in Collections: | Articles to be qced |
Files in This Item:
File | Size | Format | |
---|---|---|---|
Hyperelliptic curves over F q and Gaussian.pdf Restricted Access | 477.51 kB | Adobe PDF | View/Open Request a copy |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.