01.01.06 (Mathematical logic, algebra, and number theory)
Keywords:
L-functions,
spectral theory of automorphic forms.
Subject:
Analytic number theory
Main publications:
Olga Balkanova, “The shifted fourth moment of automorphic L-functions of prime power level”, Acta Arithmetica, 174 (2016), 121-174
Olga Balkanova, Dmitry Frolenkov, “The mean value of symmetric square L-functions”, Algebra and Number theory, 12 (2018), 35-59
Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov, Nicole Raulf, “Mixed moment of GL(2) and GL(3) L-functions”, Proceedings of the London Mathematical Society, 121:2 (2020), 177-219
Olga Balkanova, Bingrong Huang, Anders Södergren, “Non-vanishing of Maass form $L$-functions at the central point”, Proc. Amer. Math. Soc., 149:2 (2021), 509–523; (Published online)
2.
Olga Balkanova, Dmitry Frolenkov, “Moments of $L$-functions and the Liouville–Green method”, J. Eur. Math. Soc. (JEMS), 2021, 1–51 (Published online) , arXiv: 1610.03465;
3.
Olga Balkanova, Dmitry Frolenkov, “The second moment of symmetric square $L$-functions over Gaussian integers”, Proc. R. Soc. Edinb., Sect. A, Math., 2021, 1–27 (Published online) , arXiv: 2008.13399;
2020
4.
O. Balkanova, G. Bhowmik, D. Frolenkov, N. Raulf, “Mixed moment of $GL(2)$ and $GL(3)$$L$-functions”, Proc. London Math. Soc. (3), 121:2 (2020), 177–219;
5.
Olga Balkanova, “The first moment of Maass form symmetric square $L$-functions”, Ramanujan J., 2020, 1–19 (Published online) ; (Published online)
6.
Olga Balkanova, Dmitry Frolenkov, “Prime geodesic theorem for the Picard manifold”, Adv. Math., 375 (2020), 107377 , 42 pp., arXiv: 1804.00275 (cited: 1);
2019
7.
Olga Balkanova, Dmitry Frolenkov, “Bounds for a spectral exponential sum”, J. London Math. Soc., 99:2 (2019), 249–272 , arXiv: 1803.04201 (cited: 7) (cited: 7)
8.
Olga Balkanova, Dmitry Frolenkov, “Sums of Kloosterman sums in the prime geodesic theorem”, Q. J. Math., 70:2 (2019), 60, 649–674 , 27 pp., arXiv: 1803.04206 (cited: 2) (cited: 2)
9.
Olga Balkanova, Dimitrios Chatzakos, Giacomo Cherubini, Dmitry Frolenkov, Niko Laaksonen, “Prime geodesic theorem in the 3-dimensional hyperbolic space”, Trans. Amer. Math. Soc., 372:8 (2019), 5355–5374 , arXiv: 1712.00880 (cited: 3) (cited: 5)
10.
Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov, Nicole Raulf, “A mean value result for a product of $GL(2)$ and $GL(3)$$L$-functions”, Mathematika, 65:3 (2019), 743–762 , arXiv: 1710.01388 (cited: 1) (cited: 1)
11.
Olga Balkanova, Dmitry Frolenkov, “Convolution formula for the sums of generalized Dirichlet L-functions”, Rev. Mat. Iberoam., 35:7 (2019), 1973–1995 (cited: 1) (cited: 1)
2018
12.
Olga Balkanova, Dmitry Frolenkov, “Non-vanishing of automorphic $L$-functions of prime power level”, Monatsh. Math., 185:1 (2018), 17–41 , arXiv: 1605.02434 (cited: 1) (cited: 1)
13.
Olga Balkanova, Dmitry Frolenkov, “The mean value of symmetric square $L$-functions”, Algebra Number Theory, 12:1 (2018), 35–59 , arXiv: 1610.06331 (cited: 6) (cited: 6)
2017
14.
Olga Balkanova, Dmitry Frolenkov, “New error term for the fourth moment of automorphic $L$-functions”, J. Number Theory, 173 (2017), 293–303 (cited: 2) (cited: 2)
15.
Olga G. Balkanova, Dmitry A. Frolenkov, “On the binary additive divisor problem”, Proc. Steklov Inst. Math., 299 (2017), 44–49 (cited: 1) (cited: 1)
16.
Olga Balkanova, Dmitry Frolenkov, “The first moment of cusp form $L$-functions in weight aspect on average”, Acta Arith., 181:3 (2017), 197–208 , arXiv: 1703.00742 (cited: 1) (cited: 1)
2016
17.
Olga G. Balkanova, Dmitry A. Frolenkov, “A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line”, Proc. Steklov Inst. Math., 294 (2016), 13–46 (cited: 5) (cited: 4)
18.
Olga Balkanova, “The shifted fourth moment of automorphic L-functions of prime power level”, Acta Arith., 174 (2016), 121–174 (cited: 1) (cited: 1)
2021
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