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20162020
most citedPrime geodesics and averages of the Zagier -series

1 citations · 1 across the 3 of their papers we have counts for

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math.NT2020

Spectral decomposition formula and moments of symmetric square L-functions

Olga Balkanova

We prove a spectral decomposition formula for averages of Zagier L-series in terms of moments of symmetric square L-functions associated to Maass and holomorphic cusp forms of leve…

math.NT2019★ 1 cited

Prime geodesics and averages of the Zagier -series

Olga Balkanova, Dmitry Frolenkov, Morten S. Risager

The Zagier -series encode data of real quadratic fields. We study the average size of these -series, and prove asymptotic expansions and omega results for the expansion. We t…

math.NT2019

The first moment of Maass form symmetric square L-functions

Olga Balkanova

We prove an asymptotic formula for the twisted first moment of Maass form symmetric square L-functions on the critical line and at the critical point. The error term is estimated u…

math.NT2018

Mixed moment of and -functions

Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov +1

Let run over the space of primitive cusp forms of level one and weight , . We prove an explicit formula for the mixed moment of the Hec…

math.NT2018

Non-vanishing of Maass form L-functions at the critical point

Olga Balkanova, Bingrong Huang, Anders Södergren

In this paper, we consider the family of -functions associated to an orthonormal basis of even Hecke-Maass forms for the mod…

math.NT2018

Prime geodesic theorem for the Picard manifold

Olga Balkanova, Dmitry Frolenkov

Let be the Picard group and be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient , called the Picar…