Exact values of Γ∗(10,p)

Author:

Veras Daiane S.1,Rodrigues Paulo H. A.2

Affiliation:

1. Instituto Federal de Goiás, IFG, BR-040, km 6, Avenida Saia Velha, S/N, Area 8, Parque Esplanada V, Valparaíso de Goiás, CEP 72876-601, GO, Brazil

2. Instituto de Matemática e Estatística, UFG, Campus Samambaia, Goiânia, CEP 74690-90, GO, Brazil

Abstract

For [Formula: see text] and [Formula: see text] a prime number, define [Formula: see text] to be the smallest positive integer [Formula: see text] such that any diagonal form [Formula: see text], with integer coefficients, has nontrivial zero over [Formula: see text] whenever [Formula: see text]. A special case of a conjecture attributed to Artin states that [Formula: see text]. It is well known that the equality occurs when [Formula: see text]. In this paper, we obtain the exact values of [Formula: see text] for all primes [Formula: see text] and, except for [Formula: see text], these values are much lower than those established in the conjecture, as might be expected.

Funder

CNPq

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

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