19 citations · 90 across the 13 of their papers we have counts for
13 papers
Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function
Andrius Grigutis, Yuri Matiyasevich, Lukas Turčinskas
We prove four explicit continued fraction representations for the Lerch transcendent , where and . All of the continu…
Mathematical Proof Between Generations
Jonas Bayer, Christoph Benzmüller, Kevin Buzzard +7
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This…
On Diophantine equations over with unknowns
Yuri Matiyasevich, Zhi-Wei Sun
In this paper we show that there is no algorithm to decide whether an arbitrarily given polynomial equation (with integer coefficients) over the Gaussian r…
Congruences for Apéry numbers
Hui-Qin Cao, Yuri Matiyasevich, Zhi-Wei Sun
In this paper we establish some congruences involving the Apéry numbers . For example, we show that $$\sum_{k=0…
Approximation of Riemann's zeta function by finite Dirichlet series: multiprecision numerical approach
Gleb Beliakov, Yuri Matiyasevich
The finite Dirichlet series from the title are defined by the condition that they vanish at as many initial zeroes of the zeta function as possible. It turned out that such series…
A Parallel Algorithm for Calculation of Large Determinants with High Accuracy for GPUs and MPI clusters
Gleb Beliakov, Yuri Matiyasevich
We present a parallel algorithm for calculating very large determinants with arbitrary precision on computer clusters. This algorithm minimises data movements between the nodes and…