Algebraic Number Theory
《Algebraic Number Theory》 · 第 410–411 页 · Section 12.2「Weil's explicit formula」，Theorem 12.13
In order to see better the relationship between a sum over zeros and a corresponding sum over primes, we now derive an explicit formula that applies to a general class of kernels. Theorem 12.13 (Weil) begins: Let $F(x)$ be a measurable function such that the stated integrability and symmetry conditions hold, and put $\Phi(s)=\int_{-\infty}^{\infty}F(x)e^{-(s-1/2)2\pi x}\,dx$.