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Extra Form
강연자 David Leep
소속 Univ. of Kentucky
date 2011-03-17

It is usually a difficult problem to characterize precisely which elements of a given integral domain can be written as a sum of squares of elements from the integral domain. Let R denote the ring of integers in a quadratic number field. This talk will deal with the problem of identifying which elements of R can be written as a sum of squares. If an element in R can be written as a sum of squares, then the element must be totally positive. This necessary condition is not always sufficient. We will determine exactly when this necessary condition is sufficient. In addition, we will develop several criteria to guarantee that a representation as a sum of squares is possible. The results are based on theorems of I. Niven and C. Siegel from the 1940's, and R. Scharlau from 1980.

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첨부 '1'
List of Articles
카테고리 제목 소속 강연자
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수학강연회 Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
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수학강연회 The Shape of Data file Stanford University Gunnar E. Carlsson
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수학강연회 Quantum Dynamics in the Mean-Field and Semiclassical Regime file Ecole Polytechnique Francoise Golse
수학강연회 Entropies on covers of compact manifolds file CNRS (France) François Ledrappier
수학강연회 Sums of squares in quadratic number rings file Univ. of Kentucky David Leep
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