Jonathan Sondow

Affiliation: New York

Email: jsondow@alumni.princeton.edu

Title Of Talk: Ramanujan, Robin, the Riemann Hypothesis, and recent developments

URLS:
www.integers-ejcnt.org/l33/l33.Abstract.html
arxiv.org/abs/1112.6010

Abstract: First I will tell the story of how the hidden part of Ramanujan's thesis ``Highly composite numbers'' was discovered by Jean-Louis Nicolas at the Ramanujan 100 Conference at Urbana in 1987. Then I will explain the part on an asymptotic upper bound for the sum-of-divisors function, which Ramanujan proved assuming the Riemann Hypothesis (RH). Next I will state the non-asymptotic version equivalent to RH proved in 1984 by Guy Robin, whose thesis advisor was Nicolas. Finally I will describe recent related criteria for RH proved jointly with Geoffrey Caveney and Nicolas. See http://www.integers-ejcnt.org/l33/l33.Abstract.html and http://arxiv.org/abs/1112.6010 for details.

Last update made Tue Jul 24 15:36:14 EDT 2012.
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