Comparing zeros of distinct Dirichlet L-functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929347265298432 |
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| author | Banks, William D. |
| author_facet | Banks, William D. |
| contents | For any $θ>\frac13$, we show that there are constants $c_1,c_2>0$ that depend only on $θ$ for which the following property holds. If $χ_1,χ_2$ are two distinct primitive Dirichlet characters modulo $q$, and $T\ge c_1q^θ$, then $L(s,χ_1)$ and $L(s,χ_2)$ do not have the same zeros in the region $$\big\{s=σ+it\in{\mathbb C}:0<σ<1,~T<t<T+c_2q^θ\log T\big\}.$$ For cubefree moduli $q$, the same result holds for any $θ>\frac14$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07073 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparing zeros of distinct Dirichlet L-functions Banks, William D. Number Theory 11M06, 11M26 For any $θ>\frac13$, we show that there are constants $c_1,c_2>0$ that depend only on $θ$ for which the following property holds. If $χ_1,χ_2$ are two distinct primitive Dirichlet characters modulo $q$, and $T\ge c_1q^θ$, then $L(s,χ_1)$ and $L(s,χ_2)$ do not have the same zeros in the region $$\big\{s=σ+it\in{\mathbb C}:0<σ<1,~T<t<T+c_2q^θ\log T\big\}.$$ For cubefree moduli $q$, the same result holds for any $θ>\frac14$. |
| title | Comparing zeros of distinct Dirichlet L-functions |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2302.07073 |