SMS scnews item created by John Enyang at Sun 17 Mar 2013 1904
Type: Seminar
Modified: Sun 17 Mar 2013 1905
Distribution: World
Expiry: 23 Mar 2013
Calendar1: 22 Mar 2013 1205-1255
Auth: enyang@penyang.pc (assumed)

# Numerical testing of the Riemann Hypothesis

### Donovan

###### Speaker:

Peter Donovan (UNSW)

###### Title:

Numerical testing of the Riemann Hypothesis

###### Abstract:

A sequence of remarkably successful calculations has shown that the first 100,000,000,000 zeros of the zeta function $$\zeta(s)$$ in the upper half of the strip $$0 < \mathfrak{R}(s) < 1$$ have real part $$\frac{1}{2}$$. This talk outlines a quite independent method of testing the Riemann Hypothesis (RH). André Weil's quadratic functional (1953) on a suitable space of functions on the group of positive real numbers can be evaluated for what have to pass for step functions and the positive deniteness of some of a family of symmetric matrices determined. If any of these turned out not to be positive denite the RH would be disproved. No such example was found! Conversely, if all of these are shown to be positive denite the RH would have been verifed.

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We will take the speaker to lunch after the talk.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang John.Enyang@sydney.edu.au

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