### Mathematics Colloquium

# Yuri Matiyasevich

### (St. Petersburg Department of Steklov Institute of Mathematics)

## "Finite Dirichlet series with partially prescribed zeroes"

** Date: ** |
Thu, October 19, 2017 |

** Time: ** |
16:00 |

** Place: ** |
The talk will be given at University Bremen. MZH building, room 6120 |

**Abstract:** 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 \((1-2\cdot 2^{-s})\zeta(s)\) 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 coecients of such series encode prime numbers in several ways.

*The colloquium is preceded by tea from 15:30 in the 6345 Room.*