All this seems to be started by Georg Friedrich Bernhard Riemann’s original paper whose English translation was included at least in [12], without, however forgetting the enormous influence of Leonhard Euler and his studies on the function now known as the Riemann zeta-function. After this, a huge number of papers is available in the internet on the Riemann hypothesis and the zeta-function. Fur...

Within the variegated framework of Riemann zeta function and related conjecture (Riemann Hypothesis), we would like to start with a study of some quite disregarded or not much in-deep studied historical aspects concerning Entire Function Theory aspects of Riemann zeta function. This first paper essentially would be the manifesto of such a historical research program whose main points will be in...

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices. Our approach is based on the finite gap integration method applied to study the Riemann-Hilbert by Kitaev and Korotkin [1], Deift, Its, Kapaev and Zhou [2] and Korotkin, [3]. This permits us to solve the Riemann-Hilbert prob...

A two-dimensional Riemann solver is proposed for the solution of hyperbolic systems of conservation laws in two dimensions of space. The solver approximates the solution of a so-called angular two-dimensional Riemann problem as the weighted sum of the solutions of one-dimensional Riemann problems. The weights are proportional to the aperture of the regions of constant state. The two-dimensional...