Prime values of Ramanujan's tau function
| Autor: | Xiong, Boyuan |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the prime values of Ramanujan's tau function $\tau(n)$. Lehmer found that $n=251^2=63001$ is the smallest $n$ such that $\tau(n)$ is prime: $$\tau(251^2)=-80561663527802406257321747.$$ We prove that in most arithmetic progressions (mod 23), the prime values $\tau$ belonging to the progression form a thin set. As a consequence, there exists a set of primes of Dirichlet density $\frac{9}{11}$ which are not values of $\tau$. Comment: Want to renew a citation |
| Databáze: | arXiv |
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