Timeline for hyperelliptic curves over finite fields
Current License: CC BY-SA 3.0
4 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Feb 13, 2013 at 2:35 | comment | added | Michael Zieve | A peripheral remark: all the known improvements of Weil's bound in the case of hyperelliptic curves over prime fields are done via variants of Stepanov's method, which is based on the construction of an auxiliary rational function of fairly small degree which vanishes to high order at the rational points. I can't find a statement of Stark's result online, but I do see on page 15 of Stohr-Voloch "Weierstrass points..." that Stark's bound can be deduced via their geometric approach to constructing these auxiliary functions. | |
Feb 13, 2013 at 1:17 | comment | added | Felipe Voloch | @Mike: Thanks. I guess I misconstrued what you said. BTW, the answer you deleted had some additional useful information. | |
Feb 13, 2013 at 1:00 | comment | added | Michael Zieve | Felipe, maybe this is what Stark did, but for prime fields you can improve the estimate provided by the Weil bound (for the genus of a pointless hyperelliptic curve) by a factor of $\sqrt{2}$. This was done by Mitkin 1975 "Existence of rational points...", El Baghdadi 1995, and Zannier 1998 "Polynomials modulo $p$...". | |
Feb 13, 2013 at 0:34 | history | answered | Felipe Voloch | CC BY-SA 3.0 |