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):

The first moment of symmetric square L-functions related to modular forms, Mat. Sb., to appear, link
Asymptotics of a Gauss hypergeometric function related to moments of symmetric square L-functions I, Mat. zametki, to appear, link
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 203 (2024), 733– 764, link
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 the analytic theory of ternary cubic forms (with W. Duke, D. Frolenkov)
Hybrid subconvexity for Maass form symmetric square L-functions (with D. Frolenkov), arXiv
A diophantine divisor problem and Hecke zeta functions (with W. Duke, D. Frolenkov)
On Weyl's subconvex bound for cube-free Hecke characters: totally real case (with D. Frolenkov, H. Wu), arXiv

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