# 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):**

Prime geodesics and averages of the Zagier L-series (with D. Frolenkov and M.S. Risager),

*Mathematical Proceedings of the Cambridge Philosophical Society,*published online, linkThe second moment of symmetric square L-functions over Gaussian integers (with D. Frolenkov),

*Proceedings of the Royal Society of Edinburgh Section A Mathematics*, published online, linkThe first moment of Maass form symmetric square L-functions,

*The Ramanujan Journal*, published online, linkNon-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, linkMoments of L-functions and the Liouville-Green method (with D. Frolenkov),

*Journal of the European Mathematical Society (JEMS)*23:4 (2021), 1333-1380, linkNon-vanishing of Maass form symmetric square L-functions (with D. Frolenkov),

*Journal of Mathematical Analysis and Applications 500:2 (2021)**,*125148, linkPrime Geodesic Theorem for the Picard manifold (with D. Frolenkov),

*Advances in Mathematics*, 375 (2020), 107377, linkMixed 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, linkA 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, linkSums of Kloosterman sums in the prime geodesic theorem (with D. Frolenkov),

*The Quarterly Journal of Mathematics*, 70:2 (2019), pp. 649–674, linkPrime 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, linkConvolution formula for the sums of generalized Dirichlet L-functions (with D. Frolenkov),

*Revista Matemática Iberoamericana*, 35:7 (2019), pp. 1973–1995, linkBounds for a spectral exponential sum (with D. Frolenkov),

*Journal of the London Mathematical Society*, 99:2 (2019), pp. 249-272, linkThe mean value of symmetric square L-functions (with D. Frolenkov),

*Algebra and Number Theory*, 12 (2018), pp. 35-59, linkNon-vanishing of automorphic L-functions of prime power level (with D. Frolenkov),

*Monatshefte für Mathematik*, 185:1 (2018), pp. 17-41, linkThe first moment of cusp form L-functions in weight aspect on average (with D. Frolenkov),

*Acta Arithmetica*, 181:3 (2017), pp. 197-208, linkA note on the binary additive divisor problem (with D. Frolenkov),

*Proceedings of the Steklov Institute of Mathematics,*special issueNew error term for the fourth moment of automorphic L-functions (with D. Frolenkov),

*Journal of Number Theory*173 (2017), pp. 293-303*,*linkA 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, linkThe shifted fourth moment of automorphic L-functions of prime power level,

*Acta Arithmetica*174 (2016), pp. 121-174*,*link

** Preprints:**

Spectral decomposition formula and moments of symmetric square L-functions, arXiv

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