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Extra Form
Lecturer David Leep
Dept. Univ. of Kentucky
date Mar 17, 2011

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.

Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Sheaf quantization of Hamiltonian isotopies and non-displacability problems file Kyoto Univ./서울대학교 Masaki Kashiwara
Math Colloquia Solver friendly finite element methods file Oklahoma State Univ. 구자언
Math Colloquia Space.Time.Noise file Meijo University Takeyuki Hida
Math Colloquia Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures file 인하대학교 강현배
Math Colloquia Structural stability of meandering-hyperbolic group actions file 제주대학교 김성운
Math Colloquia Structures of Formal Proofs file 경북대학교 정주희
Math Colloquia Study stochastic biochemical systems via their underlying network structures file 포항공과대학교 김진수
Math Colloquia Subgroups of Mapping Class Groups file 서울대학교 김상현
Math Colloquia Subword complexity, expansion of real numbers and irrationality exponents file 동국대 김동한
Math Colloquia Sums of squares in quadratic number rings file Univ. of Kentucky David Leep
Math Colloquia Symmetry Breaking in Quasi-1D Coulomb Systems file 서강대학교 Paul Jung
Math Colloquia Symplectic Geometry, Mirror symmetry and Holomorphic Curves file 연세대 수학과 홍한솔
Math Colloquia Symplectic topology and mirror symmetry of partial flag manifolds file 부산대학교 수학과 김유식
Math Colloquia The classification of fusion categories and operator algebras file Kyoto University Masaki Izumi
Math Colloquia The Lagrange and Markov Spectra of Pythagorean triples file 동국대학교 김동한
Math Colloquia The Mathematics of the Bose Gas and its Condensation file KAIST 이지운
Math Colloquia The phase retrieval problem file Hong Kong University of Science and Technology Yang Wang
Math Colloquia The process of mathematical modelling for complex and stochastic biological systems file KAIST 김재경
Math Colloquia The Shape of Data file Stanford University Gunnar E. Carlsson
Math Colloquia The significance of dimensions in mathematics file Kyoto Univ./서울대학교 Heisuke Hironaka
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