On the Size of the Riemann zeta-Function at Places Symmetric with Respect to the Point 1/2

摘要

Improvement is made on and a simpler proof provided of a result of R. Spira which is to appear in the Duke Mathematical Journal. This result is that if s = sigma + it and zeta is the Riemann zeta-function, then absolute value (zeta (1 - s))> absolute value (zeta (s)) for all s other than zeros of zeta provided t > 1/2. The proof uses Stirling's formula, as did Spira's.