References & Citations
Mathematics > Number Theory
Title: Failures of integral Springer's Theorem
(Submitted on 19 Apr 2024)
Abstract: We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed.
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