Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the exact location of the non-trivial zeros of Riemann's zeta function

100%

Arias de Reyna J., van de Lune J.

Acta Arithmetica

2014

tom 163

nr 3

215-245

We introduce the real valued real analytic function κ(t) implicitly defined by $e^{2πiκ(t)} = -e^{-2iϑ(t)} (ζ'(1/2-it))/(ζ'(1/2+it))$ (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann's ζ(s) and ζ'(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.

Ograniczanie wyników

1 Acta Arithmetica

1 Arias de Reyna J.

1 van de Lune J.

1 2014

Wyniki wyszukiwania

On the exact location of the non-trivial zeros of Riemann's zeta function