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Monday, May 16, 2016 — 3:30 PM EDT

Joint Pure Math and Computational Mathematics Colloquium

Monday, May 16th

DC 1302 - Refreshments at 3:30pm, Talk at 4:00pm

Yuri V. Matiyasevich St.Petersburg Department of V. A. Steklov Institute of Mathematics, Russia

"Computer experiments for approximating Riemann's zeta function by finite Dirichlet series"


In 2011 the speaker began to work with nite Dirichlet series of length
N vanishing at N1 initial non-trivial zeroes of Riemann's zeta function.
Intensive multiprecision calculations revealed several interesting phenom-
ena. First, such series approximate with great accuracy the values of the
product (1 2 2 s)(s) for a large range of s lying inside the critical
strip and to the left of it (even better approximations can be obtained
by dealing with ratios of certain finite Dirichlet series). In particular the
series vanish also very close to many other non-trivial zeroes of the zeta
function (initial non-trivial zeroes \know about" subsequent non-trivial
zeroes). Second, the coecients of such series encode prime numbers in
several ways.
So far no theoretical explanation was given to the observed phenom-
ena. The ongoing research can be followed at
http://logic.pdmi.ras.ru/~yumat/personaljournal/finitedirichlet

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