Infinite Product of the Riemann auxiliary function

2024/06/18 by de Reyna, Juan Arias
#FOS: Mathematics #Number Theory (math.NT) #Primary 11M06 #Secondary 30D99

paper · doi:10.48550/arxiv.2406.12344

Abstract

We obtain the product for the auxiliary function \mathop\mathcal R(s) and study some related functions as its phase ω(t) at the critical line. The function ω(t) determines the zeros of ζ(s) on the critical line. We study the influence of the zeros of \mathop\mathcal R(s) on ω(t). Thus, the relationship between the zeros of \mathop\mathcal R(s) and those of ζ(s) is determined.

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