We prove that a quintic form in 26 variables defined over a p-adic field K always has a nontrivial zero over K if the residue class field of K has at least 47 elements. This is in agreement with the theorem of Ax Kochen which states that a homogeneous form of degree d in d 2 +1 variables defined ove
Character Sums overp-adic Fields
β Scribed by Wen-Ching Winnie Li
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 359 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
β¦ Synopsis
that ' v has conductor v. In conclusion, for f =P v , the conductor of the associated ' at v is p r&1 v. Since ' /, f is multiplicative in f, for a general f
π SIMILAR VOLUMES
## Abstract In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo __p__^__l__^ , a power of a prime. We show that for sufficiently large __l__, these sums can be expressed in terms of Gauss sums. Moreover, we study the a
Consider an extension field F q m =F q (a) of the finite field F q . Davenport proved that the set F q +a contains at least one primitive element of F q m if q is sufficiently large with respect to m. This result is extended to certain subsets of F q +a of cardinality at least of the order of magnit
The purpose of this paper is to extend results of Stepanov (1980;1994) about lower bounds for incomplete character sums over a prime finite field F p to the case of arbitrary finite field F q .
Karl M. Kronstein Department of Mathematics, Unitersity of Notre Dame, Notre Dame, Indiana 46556 AND Mark S. Mazur Departmem of Mathematics and Computer Science, Duquesne University, Pittshurgh, Pennsyhania 15282 Communicated by walter Feit Received February 15, 1985 ## INTRODUCTION In this p