arXiv subjects
Publications and source records attributed to Olga Balkanova.
In this paper various analytic techniques are com- bined 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.
We study the asymptotic behaviour of the twisted first moment of central $L$-values associated to cusp forms in weight aspect on average. Our estimate of the error term allows extending the logarithmic length of mollifier $Δ$ up to 2. The best previously known result, due to Iwaniec and Sarnak, was $Δ<1$. The proof is based on a representation formula for the error in terms of Legendre polynomials.
In this note we show that the methods of Motohashi and Meurman yield the same upper bound on the error term in the binary additive divisor problem. With this goal, we improve an estimate in the proof of Motohashi.
This paper studies the first moment of symmetric-square $L$-functions at the critical point in the weight aspect. Asymptotics with the best known error term $O(k^{-1/2})$ were obtained independently by Fomenko in 2005 and by Sun in 2013. We prove that there is an extra main term of size $k^{-1/2}$ in the asymptotic formula and show that the remainder term decays exponentially in $k$. The twisted first moment was evaluated asymptotically by Ng Ming Ho with the error bounded by $lk^{-1/2+ε}$. We improve the error bound to $l^{5/6+ε}k^{-1/2+ε}$ unconditionally and to $l^{1/2+ε}k^{-1/2}$ under the Lindelöf hypothesis for quadratic Dirichlet $L$-functions.
Iwaniec and Sarnak showed that at the minimum 25% of L-values associated to holomorphic newforms of fixed even integral weight and level $N \rightarrow \infty$ do not vanish at the critical point when N is square-free and $ϕ(N)\sim N$. In this paper we extend the given result to the case of prime power level $N=p^ν$, $ν\geq 2$.
We prove an asymptotic formula for the second moment of automorphic L-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift and twist.
We prove the asymptotic formula for the fourth moment of automorphic $L$-functions of level $p^ν$, where $p$ is a fixed prime number and $ν\rightarrow \infty$. This paper is a continuation of work by Rouymi, who computed asymptotics of the first three moments at prime power level, and a generalization of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.
We improve the error term in the asymptotic formula for the twisted fourth moment of automorphic L functions of prime level and weight two proved by Kowalski, Michel and Vanderkam. As a consequence, we obtain a new subconvexity bound in the level aspect and improve the lower bound on proportion of simultaneous non-vanishing.