题目:  The Kaluza sign problem and related probabilistic questions

报告人：Philippe MARCHAL, CNRS & Université Paris XIII（法国国家科学研究中心、巴黎第十三大学）

时间：5月7日, 16：00

地点：东区第五教学楼5407

摘要:  Let f(t)=\sum a_n t^n be a power series with positive coefficients. Can one find a necessary and sufficient condition so that 1/f has negative coefficients, except for the constant coefficient? This looks like an undergraduate exercise but in fact, this is an open question. About a century ago, Kaluza showed that a sufficient condition is that for each n,  a_n^2 < a_{n-1}a_{n+1}. We shall discuss several aspects of this question in relation with probability theory.