**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)

### Algebra Seminar

# Numerical testing of the Riemann Hypothesis

### Donovan

###### Friday 22nd March, 12:05-12:55pm, Carslaw 373

###### 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