Table of Contents
- 1 What is the answer to Riemann hypothesis?
- 2 Who is working on Riemann hypothesis?
- 3 What is the relationship between Riemann hypothesis and prime number theorem?
- 4 What is the relation between Riemann hypothesis and asymptotic distribution?
- 5 Is it possible to prove a zeta function using Riemann’s explicit formula?
What is the answer to Riemann hypothesis?
A positive answer to the Riemann hypothesis: A new result predicting the location of zeros. In this paper, a positive answer to the Riemann hypothesis is given by using a new result that predict the exact location of zeros of the alternating zeta function on the critical strip.
Who is working on Riemann hypothesis?
Dr Kumar Eswaran first published his solution to the Riemann Hypothesis in 2016, but has received mixed responses from peers. A USD 1 million prize awaits the person with the final solution.
What Riemann hypothesis says?
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 12. It is of great interest in number theory because it implies results about the distribution of prime numbers.
What is the relationship between Riemann hypothesis and prime number theorem?
The Riemann Hypothesis is about the error term in that asymptotic equation. In this sense, they are very closely linked. As lhf writes, there is a strong link between the error estimate in the prime number theorem and the Riemann hypothesis.
What is the relation between Riemann hypothesis and asymptotic distribution?
In fact it is usually easier to start from the zeta function. The asymptotic prime number distribution has been known for over a century now. The Riemann Hypothesis is about the error term in that asymptotic equation. In this sense, they are very closely linked.
Does the distribution of prime numbers follow a regular pattern?
The distribution of such prime numbers among all natural numbers does not follow any regular pattern. However, the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function ζ (s) = 1 + 1/2s + 1/3s + 1/4s + called the Riemann Zeta function.
Is it possible to prove a zeta function using Riemann’s explicit formula?
Using Riemann’s explicit formula it would be possible to take any argument about the prime distribution and translate it relatively easily into an argument about the zeta function, so it’s not the case that formulations in terms of primes are likely to be any more amenable to proof than talking about the zeta zeros.