We consider boundary integral equations of the first kind with logarithmic kernels on smooth closed or open contours in R2. Instead of solving the first kind equations directly, we propose a fully ...

This new equation is split into a principal part, which is explicitly invertible, and a compact perturbation. Then a discrete Galerkin method that takes special advantage of the splitting of the ...

The tailored integral due to its radically improved accuracy over the Gauss' logarithmic integral, constitutes the supremum bound of estimation of the prime counting function.