A note on finite Euler product approximations of the Riemann zeta-function

Gonek, Steven

doi:10.1090/proc/12380

A note on finite Euler product approximations of the Riemann zeta-function
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by Steven M. Gonek

Proc. Amer. Math. Soc. 143 (2015), 3295-3302

DOI: https://doi.org/10.1090/proc/12380

Published electronically: April 6, 2015

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Abstract:

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.

References

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