Vortragende(r): Prof. Dr. Yuri Matiyasevich
(St.Petersburg Department of V. A. Steklov Institute of Mathematics, Russia)
In 2011 the speaker began to work with finite Dirichlet series of length N vanishing at N − 1 initial non-trivial zeroes of Riemann’s zeta function. Intensive multiprecision calculations revealed several interesting phenomena. First, such series approximate with great accuracy the values of the product (1−2·2−s)ζ(s) for a large range of s lying inside the critical strip and also 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 (informally, one can say that “initial non-trivial zeroes know about subsequent non-trivial zeroes”). Second, the coefficients of such series encode prime numbers in several ways.
So far no theoretical explanation was given to the observed phenomena. The ongoing research can be followed at
Der Sprecher ist gemeinsamer Gast mit Prof. Dierk Schleicher (Jacobs University Bremen) und wird dort am Montag 16.10. einen weiteren Kolloquiumsvortrag halten zum Thema "Hilbert’s Tenth Problem today: Main results and Open problems", siehe: http://math.jacobs-university.de/