4 papers
math.NT2026
An Enhanced Higher Green's Function on the Modular Curve
Nina Sakharova
The higher Green's functions on the modular curve are real-valued eigenfunctions of the hyperbolic Laplacian in each variable, with logarithmic singularities along t…
math.AG2018
The modular Cauchy kernel for the Hilbert modular surface
Nina Sakharova
In this paper we construct the modular Cauchy kernel on the Hilbert modular surface , i.e. the function of two variables, $(z_1, z_2) \in \mat…
math.AG2018
Modular Cauchy kernel corresponding to the Hecke curve
Nina Sakharova
In this paper we construct the modular Cauchy kernel , i.e. the modular invariant function of two variables, , with the…
math.AG2015
Convergence of the Zagier type series for the Cauchy kernel
Nina Sakharova
In 1975 prof. Don Zagier derived a preliminary formula for the trace of the Hecke operators acting on the space of cusp forms (\cite{5}, \cite{6}). Actually, it is an expression in…