Number Theory


Proof of Riemann Hypothesis

Authors: Gang tae geuk

Riemann hypothesis means that satisfying ζ(s)=0(ζ(s) means Riemann Zeta function) unselfevidenceable root's part of true numbers are 1/2. Dennis Hejhal, and John Dubisher explained this hypothesis to : "Choosed Any natural numbers(exclude 1 and constructed with two or higher powered prime numbers) then the probability of numbers that choosed number's forming prime factor become an even number is 1/2." I'll prove this explain to prove Riemann hypothesis indirectly. In binomial coefficient, C(n,0)+C(n+1)+...+C(n,n)=2^n. And C(n,1)+C(n,3)+C(n,5)+...+C(n,n) and C(n,0)+C(n,2)+C(n,4)+...+C(n,n) is 2^(n-1). If you pick up 8 prime numbers, then you can make numbers that exclude 1 and constructed with two or higher powered prime numbers, and the total amount of numbers that you made is 2^8. Same principle, if you pick the numbers in k times(k is a variable), the total amount of numbers you made is C(8,k). If k is an even number, the total amount of numbers you can make is C(8,0)+C(8,2)+...+C(8,8)-1(because we must exclude 1,same for C(8,0)), and as what i said, it equals to 2^(8-1)-1. So, the probability of the numbers that forming prime factor's numbers is an even number is 2^(8-1)-1/2^8 If there are amount of prime numbers exist, and we say that amount to n(n is a variable, as the k so), and sequence of upper works sameas we did, so the probability is 2^(n-1)/2^n. If you limits n to inf, then probability convergents to 1/2. This answer coincident with the explain above, so explain is established, same as the Riemann hypothesis is.

Comments: 1 Page.

Download: PDF

Submission history

[v1] 2019-05-25 17:36:55
[v2] 2019-05-30 09:52:05

Unique-IP document downloads: 48 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus