The prime geodesic theorem in square mean

Abstract

We strengthen the recent result of Cherubini and Guerreiro on the square mean of the error term in the prime geodesic theorem for ${\mathrm{PSL}}_2(\mathbb{Z})$. We also develop a short interval version of this result.

7 pages, LaTeX2e

References in corpus (1)

• Mean square in the prime geodesic theorem

Cited by in corpus (2)

• Euler products of Selberg zeta functions in the critical strip
• The Prime Geodesic Theorem for ${\mathrm{PSL}}_2(\mathbb{Z}[i])$ and Spectral Exponential Sums