Zeta Zeros in a Narrow Vertical Box
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914431540133888 |
|---|---|
| author | Goldston, Daniel A. Suriajaya, Ade Irma |
| author_facet | Goldston, Daniel A. Suriajaya, Ade Irma |
| contents | In 1973 Montgomery proved, assuming the Riemann Hypothesis (RH), that asymptotically at least 2/3 of zeros of the Riemann zeta-function are simple zeros. In a previous note (arXiv:2511.20059 [math.NT]) we showed how RH can be replaced with a general estimate for a double sum over zeros, and this allows one to then obtain results on zeros that are both simple and on the critical line. Here we give a simple proof based on a direct generalization of Montgomery's proof that on assuming all the zeros are in a narrow vertical box between height $T$ and $2T$ of width $b/\log T$ and centered on the critical line, then, if $b=b(T)\to 0$ as $T\to \infty$, we have asymptotically at least 2/3 of the zeros are simple and on the critical line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28104 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zeta Zeros in a Narrow Vertical Box Goldston, Daniel A. Suriajaya, Ade Irma Number Theory 11M06, 11M26 In 1973 Montgomery proved, assuming the Riemann Hypothesis (RH), that asymptotically at least 2/3 of zeros of the Riemann zeta-function are simple zeros. In a previous note (arXiv:2511.20059 [math.NT]) we showed how RH can be replaced with a general estimate for a double sum over zeros, and this allows one to then obtain results on zeros that are both simple and on the critical line. Here we give a simple proof based on a direct generalization of Montgomery's proof that on assuming all the zeros are in a narrow vertical box between height $T$ and $2T$ of width $b/\log T$ and centered on the critical line, then, if $b=b(T)\to 0$ as $T\to \infty$, we have asymptotically at least 2/3 of the zeros are simple and on the critical line. |
| title | Zeta Zeros in a Narrow Vertical Box |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2603.28104 |