# Olga Balkanova

Researcher at Steklov Mathematical Institute

Address: 8 Gubkina street, 119991 Moscow

Email: balkanova at mi-ras.ru

About: I received my PhD degree in 2015 in the framework of the ALGANT Joint Doctoral Program (Bordeaux, Milan, Montreal). During the fall 2015 I was an ICERM Postdoctoral Fellow at Brown University participating in the special semester on "Computational Aspects of the Langlands Program". After that I was a Visiting Researcher at the Institute for Applied Mathematics, Khabarovsk. For the 2016-2017 academic year I was a Senior Researcher at the University of Turku. During 2017-2019 I was a Postdoctoral Fellow at the University of Gothenburg.

Research interests:

Analytic Number theory

L-functions

Spectral theory of automorphic forms

Maass forms of half-integral weight

Kloosterman sums

Papers (published or accepted):

An approximation formula for the shifted cubic moment of automorphic L-functions in the weight aspect (with J.B. Conrey, D. Frolenkov), Canadian Journal of Mathematics, published online, link

Voronoi summation formula for non-holomorphic Maass forms of half-integral weight (with D. Frolenkov), Monatshefte für Mathematik, in press

Explicit formula for the second moment of Maass form symmetric square L-functions (with D. Frolenkov), Publicacions Matematiques 67:2 (2023), 611–660, link

Spectral decomposition formula and moments of symmetric square L-functions, Izvestiya Mathematics 87:4 (2023), 641–682 , link

Prime geodesics and averages of the Zagier L-series (with D. Frolenkov and M.S. Risager), Mathematical Proceedings of the Cambridge Philosophical Society 172:3 (2022), 705-728, link

The second moment of symmetric square L-functions over Gaussian integers (with D. Frolenkov), Proceedings of the Royal Society of Edinburgh Section A Mathematics 152:1 (2022), 54-80, link

The first moment of Maass form symmetric square L-functions, The Ramanujan Journal 55 (2021), link

Non-vanishing of Maass form L-functions at the central point (with B. Huang and A. Södergren), Proceedings of the American Mathematical Society 149 (2021), 509-523, link

Moments of L-functions and the Liouville-Green method (with D. Frolenkov), Journal of the European Mathematical Society (JEMS) 23:4 (2021), 1333-1380, link

Non-vanishing of Maass form symmetric square L-functions (with D. Frolenkov), Journal of Mathematical Analysis and Applications 500:2 (2021), 125148, link

Prime Geodesic Theorem for the Picard manifold (with D. Frolenkov), Advances in Mathematics, 375 (2020), 107377, link

Mixed moment of GL(2) and GL(3) L-functions (with G. Bhowmik, D. Frolenkov and N. Raulf), Proceedings of the London Mathematical Society, 121:2 (2020), pp. 177-219, link

A mean value result for a product of GL(2) and GL(3) L-functions (with G. Bhowmik, D. Frolenkov and N. Raulf), Mathematika, 65:3 (2019), pp. 743-762, link

Sums of Kloosterman sums in the prime geodesic theorem (with D. Frolenkov), The Quarterly Journal of Mathematics, 70:2 (2019), pp. 649–674, link

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space (with D. Chatzakos, G. Cherubini, D. Frolenkov and N. Laaksonen), Transactions of the American Mathematical Society, 372 (2019), pp. 5355–5374, link

Convolution formula for the sums of generalized Dirichlet L-functions (with D. Frolenkov), Revista Matemática Iberoamericana, 35:7 (2019), pp. 1973–1995, link

Bounds for a spectral exponential sum (with D. Frolenkov), Journal of the London Mathematical Society, 99:2 (2019), pp. 249-272, link

The mean value of symmetric square L-functions (with D. Frolenkov), Algebra and Number Theory, 12 (2018), pp. 35-59, link

Non-vanishing of automorphic L-functions of prime power level (with D. Frolenkov), Monatshefte für Mathematik, 185:1 (2018), pp. 17-41, link

The first moment of cusp form L-functions in weight aspect on average (with D. Frolenkov), Acta Arithmetica, 181:3 (2017), pp. 197-208, link

A note on the binary additive divisor problem (with D. Frolenkov), Proceedings of the Steklov Institute of Mathematics, special issue dedicated to the 80th anniversary of A.A. Karatsuba, 299:1 (2017), pp. 44-49, link

New error term for the fourth moment of automorphic L-functions (with D. Frolenkov), Journal of Number Theory 173 (2017), pp. 293-303, link

A uniform asymptotic formula for the second moment of primitive L-functions on the critical line (with D. Frolenkov), Proceedings of the Steklov Institute of Mathematics 294 (2016), pp. 20-53, link

The shifted fourth moment of automorphic L-functions of prime power level, Acta Arithmetica 174 (2016), pp. 121-174, link

Preprints:

On Weyl's subconvex bound for cube-free Hecke characters: totally real case (with D. Frolenkov, H. Wu), arXiv