SEVERAL RESULTS ASSOCIATED WITH THE RIEMANN ZETA FUNCTION

• 발행기관: 충청수학회
• 저자명: June sang Choi
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 22, No. 3, 467~480쪽, 전체 14쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2009.09.30

영문 초록

In 1859, Bernhard Riemann, in his epoch-making mem-oir, extended the Euler zeta function ³(s) (s > 1; s 2 R) to the Riemann zeta function ³(s) (<(s) > 1; s 2 C) to investigate the pattern of the primes. Sine the time of Euler and then Riemann, the Riemann zeta function ³(s) has involved and appeared in a variety of mathematical research subjects as well as the function itself has been being broadly and deeply researched. Among those things, we choose to make a further investigation of the following subjects: Evaluation of ³(2k) (k 2 N); Approximate functional equations for ³(s); Series involving the Riemann zeta function.

목차

1. Introduction and Preliminaries

2. Evaluation of ³(2k) (k 2 N)

3. Approximate Functional Equations for ³(s)

References