# Rapid computation of $L$-functions attached to Maass forms

## TL;DR

This paper introduces an efficient algorithm for computing degree-2 L-functions associated with Maass forms, enabling rapid evaluation of L-values and detailed analysis of their zeros' distribution.

## Contribution

The authors develop a novel algorithm that evaluates L-functions on the critical line in near-linear time, facilitating extensive zero distribution studies.

## Key findings

- Successfully computed many consecutive zeros of L-functions.
- Observed patterns in zero distribution consistent with conjectures.
- Demonstrated the algorithm's efficiency and accuracy.

## Abstract

Let $L$ be a degree-$2$ $L$-function associated to a Maass cusp form. We explore an algorithm that evaluates $t$ values of $L$ on the critical line in time $O(t^{1+\varepsilon})$. We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution.