Highly Uniform Prime Number Theorems
| Autor: | Kaneko, Ikuya, Thorner, Jesse |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explicitly on the available zero-free region. The class contains the Rankin-Selberg $L$-function $L(s,\pi \times \pi')$ associated to cuspidal automorphic representations $\pi$ and $\pi'$ of $\mathrm{GL}_{m}$ and $\mathrm{GL}_{m'}$, respectively. Our main result implies the first uniform prime number theorems for such $L$-functions (with analytic conductor uniformity) in complete generality. Comment: 16 pages. Incorporates referee comments. Theorem 2.6 is improved |
| Databáze: | arXiv |
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