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prime geodesic theorem

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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The second moment of symmetric square L-functions over Gaussian integers
Part of
Olga Balkanova, Dmitry Frolenkov
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 1 / February 2022

Published online by Cambridge University Press:

11 January 2021, pp. 54-80

Print publication:

February 2022
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We prove a new upper bound on the second moment of Maass form symmetric square L-functions defined over Gaussian integers. Combining this estimate with the recent result of Balog–Biro–Cherubini–Laaksonen, we improve the error term in the prime geodesic theorem for the Picard manifold.