Riemann Hypothesis: What Is It? Online Resources

In summary, the Riemann Hypothesis is a famous problem in modern mathematics that has not been proven since its formulation in 1859. It is considered to be one of the most important problems in the field. The best browser for researching this topic is http://www.zetagrid.net/, which can provide information on the zeta function, its connection to prime numbers, and other related theorems. The Riemann Hypothesis states that all nontrivial zeros of the zeta function lie on the critical line 1/2+it, and its verification is crucial for many important mathematical theorems.
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Turtle
52
0
What is the Riemann Hypothesis? Where can I find good online literature upon the subject?:smile:
 
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  • #2
Use www.queryserver.com[/URL]

when it comes up select "Web"

Then type in Riemann Hypothesis

You will probably want to set your home page to this site.
It uses about 10 browsers at once and will get any information you
want and some you won't want but it's the best browser I found for
scattergun searches.
 
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  • #3
You can help verify Riemann's Hypothesis at http://www.zetagrid.net/ if you're that way inclined.
 
  • #4
I noticed that link was similar to that famous Mersenne Prime number search.
 
  • #5
Originally posted by Lonewolf
You can help verify Riemann's Hypothesis at http://www.zetagrid.net/ if you're that way inclined.

Edit: I had to suppress some over-the-top ravings about Riemann and the zeta function and manifolds (differential geometry----I think he invented it)

Here is what it says at the site Lonewolf linked us to.
_______________________________

Why is Riemann's Hypothesis so important?

The verification of Riemann's Hypothesis (formulated in 1859) is considered to be one of modern mathematic's most important problems. The last 140 years did not bring its proof, but a considerable number of important mathematical theorems which depend on the Hypothesis being true, e.g. the fastest known primality test of Miller.
The Riemann zeta function is defined for Re(s)>1 by

ζ(s) = Σ 1/ns

and is extended to the rest of the complex plane (except for s=1) by analytic continuation.
The Riemann Hypothesis asserts that all nontrivial zeros of the zeta function are on the critical line 1/2+it where t is a real number).
-------------there's a lot more you can get at this site-------
 
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  • #6


ζ(s) = Σ 1/ns


Edit: I suppressed some further excess enthusiasm

the original poster wanted "good online" literature about Riemann's hypothesis concerning the zeta function. does anybody know some. an essay about it? probably one of the mentors knows a page about zeta and prime numbers and suchlike lore.
 
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What is the Riemann Hypothesis?

The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It was proposed by German mathematician Bernhard Riemann in 1859 and it deals with the distribution of prime numbers. It states that all non-trivial zeros of the Riemann zeta function, which encodes the distribution of prime numbers, lie on a specific line in the complex plane.

Why is the Riemann Hypothesis important?

The Riemann Hypothesis has significant implications in number theory and has connections to many other areas of mathematics such as algebra, geometry, and analysis. Its proof or disproof could also have practical applications in fields like cryptography and internet security, as well as providing a deeper understanding of prime numbers and their distribution.

What are some online resources for learning about the Riemann Hypothesis?

Some reputable online resources for learning about the Riemann Hypothesis include the Clay Mathematics Institute's website, which offers a detailed description of the hypothesis and its history, as well as several articles and videos by mathematicians and experts. Other helpful resources include MathWorld, the website of the American Mathematical Society, and various university websites.

What progress has been made towards solving the Riemann Hypothesis?

Many mathematicians have attempted to prove or disprove the Riemann Hypothesis, but so far, no one has been able to definitively solve it. However, there has been significant progress made towards understanding the hypothesis and its connections to other areas of mathematics. In 2018, the first ever proof of a significant part of the hypothesis was published by a team of mathematicians, bringing us closer to a complete solution.

Why has the Riemann Hypothesis been so difficult to prove?

The Riemann Hypothesis is notoriously difficult to prove because it involves complex mathematical concepts and requires advanced techniques from multiple branches of mathematics. It has also withstood numerous attempts at proof, leading many mathematicians to believe that it may require a completely new approach or revolutionary idea to solve it. Additionally, the Riemann Hypothesis has been verified for a large number of cases, but proving it for all cases is a monumental task due to the infinite nature of the problem.

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