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Regular version of the site

Article

Sums of Kloosterman sums in the prime geodesic theorem

Quarterly Journal of Mathematics. 2019. Vol. 70. No. 2. P. 649-674.
Balkanova O., Frolenkov D.

We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we  obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.