@article{Hemingway2023, 
author = {Xian Hemingway},
title = {The Generalized Riemann Hypothesis on elliptic complex fields},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {25772-25803},
keywords = {the elliptic complex, the normal ellipse, the function L(s, χ) and ξ(s, χ), the critical case of GRH, the Generalized Riemann Hypothesis},
url = {https://www.sciopen.com/article/10.3934/math.20231315},
doi = {10.3934/math.20231315},
abstract = {In this paper, we will introduce a new algebraic system called the elliptic complex, and consider the distribution of zeros of the function    L  (  s  ,  χ  ) in the corresponding complex plane. The key to this article is to discover the limiting case of the Generalized Riemann Hypothesis on elliptic complex fields and, taking a series of elliptic complex fields as variables, to study the ordinary properties of their distributions about the non-trivial zeros of    L  (  s  ,  χ  ). It is on the basis of these considerations that we will draw the following conclusions. First, the zeros of the function    L  (  s  ,  χ  ) on any two elliptic complex planes correspond one-to-one. Then, all non-trivial zeros of the    L  (  s  ,  χ  ) function on each elliptic complex plane are distributed on the critical line    ℜ  (  s  )  =            1      2       due to the critical case of the Generalized Riemann Hypothesis. Ultimately we proved the Generalized Riemann Hypothesis.}
}