Artículo
On the exact location of the non-trivial zeros of Riemann’s zeta function
Autor/es | Arias de Reyna Martínez, Juan
Lune, Jan van de |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2014 |
Fecha de depósito | 2016-07-01 |
Publicado en |
|
Resumen | In this paper we introduce the real valued real analytic function κ(t) implicitly
defined by
e
2πiκ(t) = −e
−2iϑ(t)
ζ
0
(
1
2 − it)
ζ
0(
1
2 + it)
, (κ(0) = −
1
2
).
By studying the equation κ(t) = n ... In this paper we introduce the real valued real analytic function κ(t) implicitly defined by e 2πiκ(t) = −e −2iϑ(t) ζ 0 ( 1 2 − it) ζ 0( 1 2 + it) , (κ(0) = − 1 2 ). By studying the equation κ(t) = n (without making any unproved hypotheses), we will show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ 0 (s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it will follow that the ordinate of the zero 1/2 + iγn of ζ(s) will be the unique solution to the equation κ(t) = n. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | info:eu-repo/grantAgreement/MINECO/MTM2012-30748 |
Cita | Arias de Reyna Martínez, J. y Van de Lune, J. (2014). On the exact location of the non-trivial zeros of Riemann’s zeta function. Acta Arithmetica, 163 (3), 215-245. |
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