# Olga Balkanova

Postdoctoral Fellow at the University of Gothenburg

**Address**: Chalmers tvärgata 3, 412 58 Göteborg

**Office**: L3087

**Email: **baolga at chalmers.se

I received my PhD degree in 2015 in the framework of the ALGANT Joint Doctoral Program (Bordeaux, Milan, Montreal). During the fall semester 2015 I was an ICERM Postdoctoral Fellow at Brown University participating in the program 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.

**Research interests**:

- Analytic Number theory
- L-functions
- Spectral theory of automorphic forms
- Maass forms of half-integral weight
- Kloosterman sums

**Papers (published or accepted):**

- 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 - Moments of L-functions and Liouville-Green method (with D. Frolenkov),
*Journal of the European Mathematical Society (JEMS)*, accepted, arXiv - Sums of Kloosterman sums in the prime geodesic theorem (with D. Frolenkov),
*The Quarterly Journal of Mathematics*, published online, 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*, published online, link - Convolution formula for the sums of generalized Dirichlet L-functions (with D. Frolenkov),
*Revista Matemática Iberoamericana*, accepted, arXiv - Bounds for a spectral exponential sum (with D. Frolenkov),
*Journal of the London Mathematical Society*, published online, 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 - 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:**

- Prime Geodesic Theorem for the Picard manifold (with D. Frolenkov), arXiv
- Non-vanishing of Maass form L-functions at the critical point (with B. Huang and A. Södergren), arXiv
- Mixed moment of GL(2) and GL(3) L-functions (with G. Bhowmik, D. Frolenkov and N. Raulf), arXiv

**Contribution to conference proceedings:**

- Pell equation and systems of quadratic equations with parameters (with K. Pravdin),
*Scientific and technical journal of information technologies, mechanics and optics*, 2(47), 2008, p. 105-112 (in Russian), link - Moments of L-functions and Liouville-Green method, Oberwolfach reports 40/2017, "Automorphic forms and Arithmetic", link