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Pairs of Additive Congruences to a Large Prime Modulus

โœ Scribed by Ivan D. Meir

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
998 KB
Volume
63
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

It is known that a system of two additive equations of degree k with greater than 4k variables has a non-trivial p-adic solution for all p>k 6 . The purpose of this paper is to improve this result to p>3k 4 . A considerable modification of the standard method of exponential sums is introduced which uses the Hasse Weil sum estimate for multiplicative characters.

1997 Academic Press

with coefficients a ij # Z, has a non-trivial p-adic solution for all p>k 2r+2 .

In the case of 2 additive equations, r=2, the theorem guarantees a non-trivial solution for all p>k 6 , with n>4k variables. See also [2].

The aim of this paper is to improve the bound to p>3k 4 . The result involves a considerable modification of the standard method of exponential article no. NT972071

๐Ÿ“œ SIMILAR VOLUMES

Stickelberger Subideals for a Prime Modu
Stickelberger Subideals for a Prime Modulus Related to Kummer-Type Congruences
โœ Takashi Agoh ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 361 KB

## Dedicated to the Memory of Taruichi Yoshioka Let p 5 be a prime, 1 a set of certain positive integers, and G a cyclic group of order p&1. In this paper we mainly investigate the special subideal I 1 ( p) (depending on 1) of the Stickelberger ideal I( p) in the group ring R p =Z p [G] (where Z p