Seminars and Colloquiums
for 2010-2011
Week of March 14, 2011
Speaker:
Professor Yasuyuki Kachi, Dept. of Mathematics, University of Kansas
With the exception of this special seminar, the University is on break this week.
If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.
If you have questions, or a date you would like to confirm, please contact Dr. Fernando Schwartz.
Monday, March 14
SPECIAL ALGEBRA SEMINAR
TIME: 1:25 p.m.
ROOM: Ayres 114
SPEAKER: Professor Yasuyuki Kachi, Dept. of Mathematics, University of Kansas
TITLE: “Stirling's formula, functional identities, and special values of Riemann's zeta function”
ABSTRACT: Stirling's formula offers ball-park estimates of the factorial numbers m ! . This three-century-old formula may be seen today as something that attracts amateur math enthusiasts, but it has actually got some interesting mathematics in it that has to do with the Riemann's zeta function. Numerous results that sharpen the Stirling's original estimates are known. Among others, the celebrated `Euler-Maclaurin version' of Stirling's formula offers an intriguing link between m ! and the Bernoulli numbers, while it has one crucial drawback. Today I would like to talk about a different formula that has satisfactory features. I would like to also offer 1. a new integral formula that expresses the Euler's constant 0.5772156.., 2. functional identity of the Riemann's zeta function and one paraphrase of the Riemann Hypothesis, and 3. a new Wallis type product expression of the number $\zeta (3) = 1/13 + 1/23 + 1/33 + 1/43 + ...$. Much of the content of the talk is joint work with my graduate student Joel Font. About three-quarter of this talk is accessible to math major undergraduate students.
Past notices:
winter break
Seminars from 2009-2010 academic year
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year