【理学院】On Numerators of Bernoulli Numbers

题  目： On Numerators of Bernoulli Numbers
时  间：2019年11月21日（周四）下午 14：30-15：30
地  点：18-918
报告人：Mehmet Cenkci，教授
摘  要：The Bernoulli numbers, which appear in many different areas of mathematics such as nul-merical analysis (e.g. the Euler -Maclaurin Summation Formula), mathematical analysis (e.g.trivial zeros of the Riemann zeta function), combinatorics (e.g. connections with combinatorialnumbers like Stirling numbers), and analytic number theory (e.g. nonvanishing of the DirichletL-function), satisfy some arithmetical properties. Being rational numbers, their denominatorsare completely determined by the von Staudt-Clausen Theorem. However, such a complete

description of their numerators is not known, although many fundamental results concerningFermat's Last Theorem rest on arithmetical properties of the numerators. We shall talk aboutsome arithmetical properties of numerators of Bernoulli numbers, in particular, about K ummercongruences, Voronoi congruences, and the results due to Frobenious, Ramanujan, and Carlitz.

报告人简介：Mehmet Cenkci先后于2001年和2007年在阿卡德尼兹大学获得硕士和博士学位，现任阿卡德尼兹大学教授。主要研究解析数论、特殊和生成函数等方向。