Bounding the Pythagoras number of a field by 2n+1

被引：0

作者：

Becher, Karim Johannes ^{[1
]}

Zaninelli, Marco ^{[1
]}

机构：

[1] Univ Antwerp, Dept Math, Middelheimlaan 1, B-2020 Antwerp, Belgium

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2024年 / 228卷 / 06期

关键词：

Sums of squares; Semilocal Bezout domain; Valuation; Quadratic form; Local-global principle; Function field in one variable; HASSE PRINCIPLE; SQUARES; SUMS;

D O I：

10.1016/j.jpaa.2023.107573

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a positive integer n, a sufficient condition on a field is given for bounding its Pythagoras number by 2n + 1. The condition is satisfied for n = 1 by function fields of curves over iterated formal power series fields over R, as well as by finite field extensions of R( (t0, t1) ). In both cases, one retrieves the upper bound 3 on the Pythagoras number. The new method presented here might help to establish more generally 2n + 1 as an upper bound for the Pythagoras number of function fields of curves over R( (t1, . . . , tn) ) and for finite field extensions of R( (t0, . . . , tn) ).(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：17

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