Explicit formula and quasicrystal definition
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910873184894976 |
|---|---|
| author | de Reyna, J. Arias |
| author_facet | de Reyna, J. Arias |
| contents | We show that the Riemann hypothesis is true if and only if the measure $$μ=-\sum_{n=1}^\infty\frac{Λ(n)}{\sqrt{n}}(δ_{\log n}+δ_{-\log n})+2\cosh(x/2)\,dx$$ is a tempered distribution. In this case it is the Fourier transform of another measure $$\mathcal{F}\Bigl(\sum_γδ_{γ/2π}-2\vartheta'(2πt)\,dt\Bigr)=μ.$$ We propose a definition of Fourier quasi-crystal to make sense of Dyson suggestion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit formula and quasicrystal definition de Reyna, J. Arias Number Theory 11M26 We show that the Riemann hypothesis is true if and only if the measure $$μ=-\sum_{n=1}^\infty\frac{Λ(n)}{\sqrt{n}}(δ_{\log n}+δ_{-\log n})+2\cosh(x/2)\,dx$$ is a tempered distribution. In this case it is the Fourier transform of another measure $$\mathcal{F}\Bigl(\sum_γδ_{γ/2π}-2\vartheta'(2πt)\,dt\Bigr)=μ.$$ We propose a definition of Fourier quasi-crystal to make sense of Dyson suggestion. |
| title | Explicit formula and quasicrystal definition |
| topic | Number Theory 11M26 |
| url | https://arxiv.org/abs/2402.10604 |