arXiv subjects

Martin Ortiz Ramirez

Publications and source records attributed to Martin Ortiz Ramirez.

2 recordsLinked to original sources

arXiv2023

Zeta functions over finite fields- An exposition of Dwork's methods

The paper reviews Dwork's p-adic analytic methods used in the Weil Conjectures. The first two chapters review a version of his proof of the rationality conjecture. The rest of the paper is devoted to Dwork's original cohomological methods, along with some p-adic functional analysis. The last chapter applies what is developed to an example of Dwork's family of hypersurfaces.

math.NT↗

arXiv2020

Lattice points in spherical segments

We study lattice points in d-dimensional spheres, and count their number in thin spherical segments. We found an upper bound depending only on the radius of the sphere and opening angle of the segment. To obtain this bound we slice the segment by hyperplanes of rational direction, and then cover an arbitrary segment with one having rational direction. Diophantine approximation can be used to obtain the best rational direction possible.

math.NT↗