SEVERAL RESULTS ASSOCIATED WITH THE RIEMANN ZETA FUNCTION

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.