The exceptional set of Goldbach problem and Linnik's constant
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909998564507648 |
|---|---|
| author | Zhao, Genheng |
| author_facet | Zhao, Genheng |
| contents | Let $E(X)$ denote the number of even integers below $X$ which are not a sum of two primes. We prove the bound $E(X)=O(X^{\frac{7}{10}})$, where the implicit constant is ineffective. The method applied here also leads to $P(q)=O(q^5)$, where $P(q)$ denotes the least prime, if it exists, in any arithmetic progression modulo $q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The exceptional set of Goldbach problem and Linnik's constant Zhao, Genheng Number Theory Let $E(X)$ denote the number of even integers below $X$ which are not a sum of two primes. We prove the bound $E(X)=O(X^{\frac{7}{10}})$, where the implicit constant is ineffective. The method applied here also leads to $P(q)=O(q^5)$, where $P(q)$ denotes the least prime, if it exists, in any arithmetic progression modulo $q$. |
| title | The exceptional set of Goldbach problem and Linnik's constant |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.05631 |