✦ LIBER ✦
Newton Polygons of L Functions Associated with Exponential Sums of Polynomials of Degree Four over Finite Fields
✍ Scribed by Shaofang Hong
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 226 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
✦ Synopsis
DEDICATED TO PROFESSOR CHAO KO ON THE OCCASION OF HIS 90TH BIRTHDAY Let F O be the "nite "eld of q elements with characteristic p and F O K its extension of degree m. Fix a nontrivial additive character of
). The corresponding ¸functions are de"ned by ¸( f, t)"exp( K S K ( f )tK/m). In this paper, we apply Dwork's method to determine the Newton polygon for the ¸function ¸( f (x), t) associated with one variable polynomial f (x) when deg f (x)"4. As an application, we also give an a$rmative answer to Wan's conjecture for the case deg f (x)"4.
) is in fact a polynomial, then one can also form the exponential sum