Algebraic Number Theory
《Algebraic Number Theory》 · 第 538 页 · Appendix D.2「The Poisson summation formula」
The formula in question asserts that under suitable conditions, $\sum_{n=-\infty}^{\infty}f(n)=\sum_{k=-\infty}^{\infty}f^*(k)$, where $f$ is a function of a real variable, and $f^*$ is its Fourier transform, $f^*(t)=\int_{\mathbb R}f(x)e(-tx)\,dx$.