Abstract
Riemann zeta function is an important tool in signal analysis and number theory. Applications of the zeta function include e.g. the generation of irrational and prime numbers. In this work we present a new accelerated series for Riemann zeta function. As an application we describe the recursive algorithm for computation of the zeta function at odd integer arguments.
Highlights
The Riemann zeta function s defined as for complex numbers s with R s 1 s 1 n 1 ns 1 p prime 1 ps (1)is an integer
Riemann zeta function is an important tool in signal analysis and number theory
In this work we present a new accelerated series for Riemann zeta function
Summary
Theorem 1: Let us suppose that s is the Riemann zeta function defined by (1). The following series converges as s 0.
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