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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 A dissipative effect on some PDEs with physical singularity file University of Wisconsin-Madison 김찬우
Math Colloquia Hamiltonian dynamics, Floer theory and symplectic topology file University of Wisconsin 오용근
Math Colloquia Idempotents and topologies file University of Waterloo Nico Spronk
Math Colloquia Brownian motion with darning and conformal mappings file University of Washington Zhen-Qing Chen
Math Colloquia Anomalous diffusions and fractional order differential equations file University of Washington Zhen-Qing Chen
Math Colloquia Unprojection file University of Warwick / 서강대 Miles Reid
Math Colloquia Iwahori-Hecke algebras and beyond file University of Picardie Jules-Verne, Amiens 김성순
Math Colloquia Seifert fiberings file University of Oklahoma 이경배
Math Colloquia Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients file University of Illinois Renming Song
Math Colloquia Nonlocal generators of jump type Markov processes file University of Bielefeld Walter Hoh
Math Colloquia Unique ergodicity for foliations file Université Paris-Sud Nessim Sibony
Math Colloquia It all started with Moser file Univ. of Wisconsin/포항공대 Paul Rabinowitz
Math Colloquia Conservation laws and differential geometry file Univ. of Wisconsin Marshall Slemrod
Math Colloquia Number theoretic results in a family file Univ. of Toronto / KIAS Kim, Henry
Math Colloquia 학부생을 위한 강연: A COMBINATORIAL FORMULA FOR INFORMATION FLOW IN A NETWORK file Univ. of Rhode Island/서울대학교 국웅
Math Colloquia Sums of squares in quadratic number rings file Univ. of Kentucky David Leep
Math Colloquia Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms file Univ. of Connecticut 이규환
Math Colloquia Topology and number theory file Univ. College London/포항공대 김민형
Math Colloquia Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields file Univ. Bremen Keivan Mallahi-Karai
Math Colloquia <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations file UNIST 배한택
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