A Wiener-Ikehara type theorem and its application to Chebyshev bounds for Beurling primes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908819739639808 |
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| author | Tranoy, Yarne Vindas, Jasson |
| author_facet | Tranoy, Yarne Vindas, Jasson |
| contents | We provide a new version of the Wiener-Ikehara theorem where one deduces bounds $$ 0< \liminf_{x\to\infty} \frac{S(x)}{e^{x}}\leq \limsup_{x\to\infty} \frac{S(x)}{e^{x}} <\infty $$ for (in particular) a non-decreasing function $S$ from a mild hypothesis on the boundary behavior of its Laplace transform on a vertical segment containing $s=1$. As an application, we establish new criteria for the validity of Chebyshev bounds for Beurling generalized prime number systems under weaker conditions than were known so far. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07690 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Wiener-Ikehara type theorem and its application to Chebyshev bounds for Beurling primes Tranoy, Yarne Vindas, Jasson Number Theory Complex Variables 11M45, 11N80 We provide a new version of the Wiener-Ikehara theorem where one deduces bounds $$ 0< \liminf_{x\to\infty} \frac{S(x)}{e^{x}}\leq \limsup_{x\to\infty} \frac{S(x)}{e^{x}} <\infty $$ for (in particular) a non-decreasing function $S$ from a mild hypothesis on the boundary behavior of its Laplace transform on a vertical segment containing $s=1$. As an application, we establish new criteria for the validity of Chebyshev bounds for Beurling generalized prime number systems under weaker conditions than were known so far. |
| title | A Wiener-Ikehara type theorem and its application to Chebyshev bounds for Beurling primes |
| topic | Number Theory Complex Variables 11M45, 11N80 |
| url | https://arxiv.org/abs/2602.07690 |