Abstract:
Riemann zeta-function has a major role in the study of distribution of primes. In this paper, inspired by the researches relating to reciprocal sums of some integer sequences, we use the elementary method and several new inequalities to study the part sums of Riemann zeta-function, and give several identities for the reciprocal sums relating to the Riemann zeta-function.
Key Words: Riemann zeta-function; Inequality; Reciprocal sums; Identity; Floor function.
2010 Mathematics Subject Classification: 11B83;11M06.
