Displaying similar documents to “Sums of squares in rings of integers with 2 inverted”

Levels of rings - a survey

Detlev W. Hoffmann (2016)

Banach Center Publications

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Let R be a ring with 1 ≠ 0. The level s(R) of R is the least integer n such that -1 is a sum of n squares in R provided such an integer exists, otherwise one defines the level to be infinite. In this survey, we give an overview on the history and the major results concerning the level of rings and some related questions on sums of squares in rings with finite level. The main focus will be on levels of fields, of simple noncommutative rings, in particular division rings, and of arbitrary...

On the sum of two squares and two powers of k

Roger Clement Crocker (2008)

Colloquium Mathematicae

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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...

Sums of Squares Coprime in Pairs

Jörg Brüdern (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.