论文标题
算术进度和半决赛编程中的素数
Primes in arithmetic progressions and semidefinite programming
论文作者
论文摘要
假设普遍的Riemann假设，我们使用Carneiro，Milinovich和Soundararajan开发的方法给出了包含给定算术进展的素数的间隔大小的渐近界限[评论。数学。 helv。 94，不。 3（2019）]。为此，我们将吉南 - 韦尔的显式公式扩展到所有dirichlet字符模型$ q \ geq 3 $上，我们将相关的极端问题减少到可以通过半决赛编程来数字解决的传达优化问题。
Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed by Carneiro, Milinovich and Soundararajan [Comment. Math. Helv. 94, no. 3 (2019)]. For this we extend the Guinand-Weil explicit formula over all Dirichlet characters modulo $q \geq 3$, and we reduce the associated extremal problems to convex optimization problems that can be solved numerically via semidefinite programming.
