Pages

Riemann Hypothesis Home

A statement of the problem

Separating the Real and Complex Portions

Separating the Even and Odd Portions

Separating the Sin and Cos Portions

The Relationships Between the Sums

Showing that the Even and Odd Sums Must Individually be 0

The Ratio Conditions Generated by the Sums

Solving the Conditions Generated by the Ratios of Sums
The Riemann Hypothesis, known as a famous conjecture in mathematics, was proposed in 1859 by Bernhard Riemann in his paper "On the number of primes less than a given magnitude." The hypothesis makes a statement about the zeroes, or roots, of the similarly named Riemann Zeta function. Roots are complex numbers in this case, and it states that the only roots that exist when the real portion of those numbers are greater than 0 and less than 1, are those where the real portion is exactly equal to 1/2.
There are numerous resources on the function and hypothesis, how they relate to other problems in mathematics, of which there are many, and the title of this page is linked to Wikipedia for quick reference. This page is dedicated to a recent attempted solution of the hypothesis based on a closely related function that is commonly used in conjunction with the Zeta function, the Dirichlet Eta function.
The solution is open to peer review. If you enjoy the solution, have questions, find errors or improvements, or wish to discuss or work on the material with the author, please contact me at the links provided on the Home or Info pages.