The prime geodesic theorem for the modular orbifold

Abstract

We establish the prime geodesic theorem for the modular orbifold with exponent $\frac{9}{13}=0.692307\cdots$ in the error term. By periodicity and Heath-Brown's quadratic large sieve, we estimate the sixth moment of the error term in an approximation to the Zagier $L$-series at $s=1$. The smooth explicit formula of Soundararajan and Young then leads to the stated exponent without recourse to subconvexity for quadratic Dirichlet $L$-functions.

arXiv comment8 pages

Cited by in corpus (1)

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