Authors: Stephen Marshall
The Riemann Hypothesis is one of the most important unresolved problems in Number Theory, it was first proposed by Bernhard Riemann, in 1859. For 160 years mathematicians have struggled with this problem to no avail. The difficulty of the Riemann Hypothesis is the main reason the hypothesis has remained unsolved. Although the Riemann Hypothesis remains unsolved, several mathematicians have proven other problems are the equivalent of the Riemann Hypothesis. In other words, if any of these equivalent criteria were solved, it would also solve the Riemann Hypothesis. Of particular interest to the author is a very elementary equivalent to the Riemann Hypothesis, Lagarias’s Elementary Version of the Riemann Hypothesis. In 2002, Jeffrey Lagarias proved that his problem is equivalent to the Riemann Hypothesis, a famous question about the complex roots of the Riemann zeta function. The beauty of the Lagarias’s Elementary Version of the Riemann Hypothesis, is that it is truly an elementary and very simple problem compared to the Riemann Hypothesis. The simplicity of Lagarias’s proof is what attracted the author to attempt to solve the Riemann Hypothesis. The author was very surprised at the simple proof he formulated using the elementary work of Lagarias. The moral of this story is that many times elementary or simple proofs exist to complex mathematical problems, this is one of those cases.
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