Riemann Hypothesis: What Is It? Online Resources

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Discussion Overview

The discussion centers around the Riemann Hypothesis, its significance in modern mathematics, and the search for online resources related to the topic. Participants explore both the hypothesis itself and avenues for further reading and verification.

Discussion Character

  • Exploratory
  • Technical explanation
  • Meta-discussion

Main Points Raised

  • The original poster seeks information on what the Riemann Hypothesis is and requests recommendations for online literature.
  • One participant suggests using a specific search engine to find information on the Riemann Hypothesis, noting its effectiveness for broad searches.
  • Another participant mentions a website that allows users to help verify the Riemann Hypothesis, drawing a parallel to the Mersenne Prime number search.
  • A participant provides a brief overview of the importance of the Riemann Hypothesis, mentioning its formulation in 1859 and its implications for various mathematical theorems, including primality testing.
  • There is a request for essays or comprehensive resources about the Riemann Hypothesis and its relation to the zeta function and prime numbers.

Areas of Agreement / Disagreement

Participants generally agree on the significance of the Riemann Hypothesis and express interest in finding quality resources. However, there is no consensus on specific literature or essays that adequately cover the topic.

Contextual Notes

Some participants express uncertainty about the depth and quality of the resources available online, and there is a mention of suppressing overly enthusiastic claims about Riemann and the zeta function.

Who May Find This Useful

Individuals interested in advanced mathematics, particularly those studying number theory or the Riemann Hypothesis, may find this discussion and the suggested resources beneficial.

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What is the Riemann Hypothesis? Where can I find good online literature upon the subject?:smile:
 
Mathematics news on Phys.org
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.
 
Last edited by a moderator:
I noticed that link was similar to that famous Mersenne Prime number search.
 
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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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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