में बचाया:
| मुख्य लेखक: | |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2024
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2402.10604 |
| टैग: |
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| _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 |