Sums of squares in $S$-integers
Sums of squares in $S$-integers
In totally real number fields, we characterize the rings of $S$-integers (obtained by inverting a rational integer $m$) such that all their totally positive elements are represented as a sum of squares. We further obtain partial answers to the question: when are all the totally positive algebraic integers that are divisible by $m$ represented as a sum of squares?
6 pages, to appear in New York J. Math
Quadratic forms over global rings and fields, Mathematics - Number Theory, Pythagoras number, number field, Quadratic extensions, 11E25, 11E12, 11R11, totally real, FOS: Mathematics, \(S\)-integers, Number Theory (math.NT), sum of squares, Sums of squares and representations by other particular quadratic forms
Quadratic forms over global rings and fields, Mathematics - Number Theory, Pythagoras number, number field, Quadratic extensions, 11E25, 11E12, 11R11, totally real, FOS: Mathematics, \(S\)-integers, Number Theory (math.NT), sum of squares, Sums of squares and representations by other particular quadratic forms
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