D. Frolenkov

activity

20162026

most citedOn the mean value of symmetric square L-functions

15 citations · 43 across the 15 of their papers we have counts for

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24 papers · 1 filter

math.NT2026

Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals

Olga Balkanova, Dmitry Frolenkov

Recently, Li obtained a mean Lindelöf estimate for the cubic moment of the central values of Maass form symmetric square $L$ -functions over short intervals $(T - H, T + H)$ of length $…

math.NT2026

Non-vanishing of symmetric square $L$ -functions in the weight aspect

Olga Balkanova, Dmitry Frolenkov

We prove a new asymptotic formula for the second moment of symmetric square L-functions in the weight aspect on average. This result implies that the associated L-function is non-v…

math.NT2024

Hybrid subconvexity for Maass form symmetric-square $L$ -functions

Olga Balkanova, Dmitry Frolenkov

Recently R. Khan and M. Young proved a mean Lindelöf estimate for the second moment of Maass form symmetric-square $L$ -functions $L (sym^{2} u_{j}, 1/2 + i t)$ on the short interva…

math.NT2024

The second moment of Maass form symmetric square L-functions at the central point

Dmitry Frolenkov

Recently R.Khan and M.Young proved a mean Lindelöf estimate on the second moment of central values of Maass form symmetric-square $L$ -function on the interval $T < ∣ t_{j} ∣ < T + T^{1/5 + ε}$ …

math.NT2024

Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square $L$ -functions II

Dmitry Frolenkov

We prove an asymptotic formula for $F (1/4 - i t + i r, 1/4 - i t - i r, 1/2; x)$ as $r, t \to \infty$ and $α = r / t \to 0.$ This special case of the Gauss hypergeometric function appears in…

math.NT2024

The shifted fourth moment of modular form L-functions in the weight aspect

Olga Balkanova, Dmitry Frolenkov

We prove a reciprocity type formula for the fourth moment of L-functions associated to holomorphic primitive cusp forms of level one and large weight which relates it to the eighth…

math.NT2021★ 1 cited

On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case

Olga Balkanova, Dmitry Frolenkov, Han Wu

We prove a Weyl-type subconvex bound for cube-free level Hecke characters over totally real number fields. Our proof relies on an explicit inversion to Motohashi's formula. Schwart…

math.NT2020★ 3 cited

The second moment of symmetric square L-functions over Gaussian integers

Olga Balkanova, Dmitry Frolenkov

We prove a new upper bound on the second moment of Maass form symmetric square L-functions defined over Gaussian integers. Combining this estimate with the recent result of Balog-B…

math.NT2019★ 1 cited

Prime geodesics and averages of the Zagier $L$ -series

Olga Balkanova, Dmitry Frolenkov, Morten S. Risager

The Zagier $L$ -series encode data of real quadratic fields. We study the average size of these $L$ -series, and prove asymptotic expansions and omega results for the expansion. We t…

math.NT2018★ 4 cited

Mixed moment of $G L (2)$ and $G L (3)$ $L$ -functions

Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov +1

Let $f$ run over the space $H_{4 k}$ of primitive cusp forms of level one and weight $4 k$ , $k \in N$ . We prove an explicit formula for the mixed moment of the Hec…

math.NT2018

Prime geodesic theorem for the Picard manifold

Olga Balkanova, Dmitry Frolenkov

Let $Γ = P S L (2, Z [i])$ be the Picard group and $H^{3}$ be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient $Γ ∖ H^{3}$ , called the Picar…

math.NT2018

Sums of Kloosterman sums in the prime geodesic theorem

Olga Balkanova, Dmitry Frolenkov

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 Yo…

math.NT2018★ 8 cited

Bounds for a spectral exponential sum

Olga Balkanova, Dmitry Frolenkov

We prove new upper bounds for a spectral exponential sum by refining the process by which one evaluates mean values of $L$ -functions multiplied by an oscillating function. In parti…

math.NT2017

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

Olga Balkanova, Dimitrios Chatzakos, Giacomo Cherubini +2

For $Γ$ a cofinite Kleinian group acting on $H^{3}$ , we study the Prime Geodesic Theorem on $M = Γ\ H^{3}$ , which asks about the asymptotic behaviour of length…

math.NT2017★ 5 cited

A Mean Value Result for a Product of GL(2) and GL(3) L-Functions

Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov +1

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…

math.NT2017

Convolution formula for the sums of generalized Dirichlet L-functions

Olga Balkanova, Dmitry Frolenkov

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…

math.NT2017

The first moment of cusp form L-functions in weight aspect on average

Olga Balkanova, Dmitry Frolenkov

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 exte…

math.NT2016

A note on the binary additive divisor problem

Olga Balkanova, Dmitry Frolenkov

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 es…

math.NT2016★ 15 cited

On the mean value of symmetric square L-functions

Olga Balkanova, Dmitry Frolenkov

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 obta…

math.NT2016

Moments of L-functions and Liouville-Green method

Olga Balkanova, Dmitry Frolenkov

We show that the percentage of primitive forms of level one and weight $4 k \to \infty$ for which the associated $L$ -function at the central point is no less than $(\log{k})^…

math.NT2016★ 5 cited

Asymptotic formulas for the second moments of $L$ -series associated to holomorphic cusp forms on the critical line

V. A. Bykovskii, D. A. Frolenkov

New uniform asymptotic formulas are obtained for the second moment of $L$ -series of cusp forms of even weight $2 k \geq 2$ with respect to the congruence subgroup $Γ_{0} (N) .$

math.NT2016

Non-vanishing of automorphic L-functions of prime power level

Olga Balkanova, Dmitry Frolenkov

Iwaniec and Sarnak showed that at the minimum 25% of L-values associated to holomorphic newforms of fixed even integral weight and level $N \to \infty$ do not vanish at the…

math.NT2016★ 1 cited

A uniform asymptotic formula for the second moment of primitive L-functions on the critical line

Olga Balkanova, Dmitry Frolenkov

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…

math.NT2016

New error term for the fourth moment of automorphic L functions

Olga Balkanova, Dmitry Frolenkov

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.…

Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals

Non-vanishing of symmetric square L-functions in the weight aspect

Hybrid subconvexity for Maass form symmetric-square L-functions

The second moment of Maass form symmetric square L-functions at the central point

Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square L-functions II

The shifted fourth moment of modular form L-functions in the weight aspect

On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case

The second moment of symmetric square L-functions over Gaussian integers

Prime geodesics and averages of the Zagier L-series

Mixed moment of GL(2) and GL(3) L-functions

Prime geodesic theorem for the Picard manifold

Sums of Kloosterman sums in the prime geodesic theorem

Bounds for a spectral exponential sum

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

A Mean Value Result for a Product of GL(2) and GL(3) L-Functions

Convolution formula for the sums of generalized Dirichlet L-functions

The first moment of cusp form L-functions in weight aspect on average

A note on the binary additive divisor problem

On the mean value of symmetric square L-functions

Moments of L-functions and Liouville-Green method

Asymptotic formulas for the second moments of L-series associated to holomorphic cusp forms on the critical line

Non-vanishing of automorphic L-functions of prime power level

A uniform asymptotic formula for the second moment of primitive L-functions on the critical line

New error term for the fourth moment of automorphic L functions

Non-vanishing of symmetric square $L$ -functions in the weight aspect

Hybrid subconvexity for Maass form symmetric-square $L$ -functions

Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square $L$ -functions II

Prime geodesics and averages of the Zagier $L$ -series

Mixed moment of $G L (2)$ and $G L (3)$ $L$ -functions

Asymptotic formulas for the second moments of $L$ -series associated to holomorphic cusp forms on the critical line