6 papers
Convolution identities for complex-indexed divisor functions and modular graph functions
Ksenia Fedosova, Kim Klinger-Logan
We find exact identities for sums of the form \begin{equation*}\label{eq:convsumabs} \sum_{\stackrel{n_1+n_2 = n}{n_1 \in \mathbb{Z} \setminus \{ 0, n \} }} Q(n_1,n_2) σ_{-r_1}(n_1…
Spectral and dynamical invariants of Hecke triangle groups via transfer operators
Ksenia Fedosova
In this paper, we consider Hecke triangle groups for and associated infinite-volume orbifolds . We show that the Selberg zeta function $Z_{Γ_…
Whittaker Fourier type solutions to differential equations arising from string theory
Ksenia Fedosova, Kim Klinger-Logan
In this article, we find the full Fourier expansion for the generalized non-holomorphic Eisenstein series for certain values of parameters. We give a connection of the boundary con…
Scattering Theory with Unitary Twists
Moritz Doll, Ksenia Fedosova, Anke Pohl
We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the appr…
Counting Resonances on Hyperbolic Surfaces with Unitary Twists
Moritz Doll, Ksenia Fedosova, Anke Pohl
We present the Laplace operator associated to a hyperbolic surface and a unitary representation of the fundamental group , extending the previous definiti…
Asymptotic expansion for the eigenvalues of a perturbed anharmonic oscillator
Ksenia Fedosova, Medet Nursultanov
In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Hölder continuous perturbation and investiga…