| 1. |
- Balkanova, Olga, 1988, et al.
(författare)
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A MEAN VALUE RESULT FOR A PRODUCT OF GL(2) AND GL(3) L-FUNCTIONS
- 2019
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Ingår i: Mathematika. - 0025-5793 .- 2041-7942. ; 65:3, s. 743-762
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Tidskriftsartikel (refereegranskat)abstract
- In this paper various analytic techniques are combined in order to study the average of a product of a Hecke L-function and a symmetric square L-function at the central point in the weight aspect. The evaluation of the second main term relies on the theory of Maass forms of half-integral weight and the Rankin-Selberg method. The error terms are bounded using the Liouville-Green approximation.
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| 2. |
- Balkanova, Olga, et al.
(författare)
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Convolution formula for the sums of generalized Dirichlet L-functions
- 2019
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230. ; 35:7, s. 1973-1995
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Tidskriftsartikel (refereegranskat)abstract
- Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet L-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square L-functions and an asymptotic expansion for the average of central values of generalized Dirichlet L-functions.
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| 3. |
- Balkanova, Olga, 1988, et al.
(författare)
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Convolution formula for the sums of generalized Dirichlet L-functions
- 2019
-
Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230 .- 2235-0616. ; 35:7, s. 1973-1995
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Tidskriftsartikel (refereegranskat)abstract
- Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet L-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square L-functions and an asymptotic expansion for the average of central values of generalized Dirichlet L-functions.
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| 4. |
- Balkanova, Olga, 1988, et al.
(författare)
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Prime geodesic theorem for the Picard manifold
- 2020
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 375
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Tidskriftsartikel (refereegranskat)abstract
- Let Γ=PSL(2,Z[i]) be the Picard group and H3 be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Γ∖H3, called the Picard manifold, obtaining an error term of size O(X3/2+θ/2+ϵ), where θ denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers.
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| 5. |
- Balkanova, Olga, 1988, et al.
(författare)
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Prime geodesic theorem in the 3-dimensional hyperbolic space
- 2019
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Ingår i: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850. ; 372:8, s. 5355-5374
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Tidskriftsartikel (refereegranskat)abstract
- For Γ a cofinite Kleinian group acting on H3, we study the prime geodesic theorem on M = Γ\H3, which asks about the asymptotic behavior of lengths of primitive closed geodesics (prime geodesics) on M. Let EΓ(X) be the error in the counting of prime geodesics with length at most log X. For the Picard manifold, Γ = PSL(2, Z[i]), we improve the classical bound of Sarnak, EΓ(X) = O(X5/3+e), to EΓ(X) = O(X13/8+e). In the process we obtain a mean subconvexity estimate for the Rankin-Selberg L-function attached to Maass-Hecke cusp forms. We also investigate the second moment of EΓ(X) for a general cofinite group Γ, and we show that it is bounded by O(X16/5+e).
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| 6. |
- Balkanova, Olga, 1988, et al.
(författare)
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Sums of Kloosterman sums in the prime geodesic theorem
- 2019
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Ingår i: Quarterly Journal of Mathematics. - : Oxford University Press (OUP). - 0033-5606 .- 1464-3847. ; 70:2, s. 649-674
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Tidskriftsartikel (refereegranskat)abstract
- We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.
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