Riemann Hypothesis: What Is It? Online Resources

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SUMMARY

The Riemann Hypothesis, formulated in 1859, is a pivotal problem in modern mathematics, asserting that all nontrivial zeros of the Riemann zeta function lie on the critical line 1/2 + it. This hypothesis underpins numerous mathematical theorems, including the fastest known primality test by Miller. Users can explore online resources such as www.queryserver.com for comprehensive literature and verification tools like http://www.zetagrid.net/ to engage with the hypothesis actively. The discussion emphasizes the importance of the zeta function and its implications in number theory.

PREREQUISITES
  • Understanding of the Riemann zeta function and its definition for Re(s) > 1.
  • Familiarity with complex analysis and analytic continuation.
  • Knowledge of number theory, particularly primality testing.
  • Basic grasp of differential geometry concepts related to manifolds.
NEXT STEPS
  • Research the implications of the Riemann Hypothesis on number theory.
  • Study the fastest known primality test by Miller in detail.
  • Explore analytic continuation techniques in complex analysis.
  • Investigate online resources and literature specifically focused on the Riemann zeta function.
USEFUL FOR

Mathematicians, number theorists, and students interested in advanced mathematical concepts, particularly those focused on the Riemann Hypothesis and its applications in number theory.

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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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