# Tag Archives: functional equations

## Functional Equations for L-Functions arising from Modular Forms

In this note, I remind myself of the functional equations for the ${L}$-functions ${\displaystyle \sum_{n\geq 0} \frac{a(n)}{n^s}}$ and ${\displaystyle \sum_{n\geq 0} \frac{a(n)}{n^s}e(\frac{n\overline{r}}{c})}$, where ${\overline{r}}$ is the multiplicative inverse of ${r \bmod c}$.