The generalized strong recurrence for non-zero rational parameters

TL;DR

This paper extends the concept of strong recurrence to all non-zero rational numbers and demonstrates its validity in the region of absolute convergence for any real number, linking it to the Riemann hypothesis.

Contribution

It proves the generalized strong recurrence for all non-zero rational numbers and in the absolute convergence region for any real number, broadening previous results.

Findings

Generalized strong recurrence holds for all non-zero rationals.

The recurrence in the absolute convergence region applies to any real number.

Links strong recurrence to the Riemann hypothesis.

Abstract

The strong recurrence is equivalent to the Riemann hypothesis. On the other hand, the generalized strong recurrence holds for any irrational number. In this paper, we show the generalized strong recurrence for all non-zero rational numbers. Moreover, we prove that the generalized strong recurrence in the region of absolute convergence holds for any real number.