A NOTE ON FINITE EULER PRODUCT APPROXIMATIONS OF THE RIEMANN ZETA-FUNCTION

摘要

We construct a family of approximations of the Riemann zeta-function and a closely related function formed from finite Euler products, the pole of the zeta-function, and any zeros the zeta-function might have in the right half of the critical strip. The analysis is unconditional and suggests that if the Riemann Hypothesis is false, then the zeta-function's zeros "arise" in two ways.