On the historical investigation of Bernoulli and Euler numbers associated with Riemann zeta functions

수학사적 관점에서 오일러 및 베르누이 수와 리만 제타함수에 관한 탐구

  • 김태균 (경북대학교 전자전기컴퓨터학부) ;
  • 장이채 (건국대학교 전산수학과)
  • Published : 2007.11.30

Abstract

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.