## Riemann hypothesis - Wikipedia, the free encyclopedia

### Riemann Hypothesis - Wikipedia | Conjecture | Analysis

Stronger statements than the Riemann hypothesis have also been formulated, but they have a tendency to be disproven. () showed that if the functions

### Hypothesis - Simple English Wikipedia, the free encyclopedia

The Riemann hypothesis has various weaker consequences as well; one is the on the rate of growth of the zeta function on the critical line, which says that, for any *ε* > 0,

A direct translation of RH (Riemann Hypothesis) would be very baffling in layman's terms. But, there are many problems that are equivalent to RH and hence, defining them would be actually indirectly stating RH. Some of the equivalent forms of RH are much easier to understand than RH itself. I give what I think is the most easy equivalent form that I have encountered:

## Riemann Hypothesis/The hypothesis - Wikibooks, open …

is valid for every *s* with real part greater than ½, with the sum on the right hand side converging, is equivalent to the Riemann hypothesis. From this we can also conclude that if the is defined by

## The Riemann Hypothesis For Dummies @ Things Of …

*Unfortunately, it looks like in this case it’s not a real proof of the Riemann Hypothesis, and this post on a Nigerian discussion forum says emphatically. As mentioned in that post, there’s under his name, which is actually a copy of a paper by someone called Werner Raab (retired). Raab’s website – is empty, and has a single broken link to “the truth of the Riemann hypothesis”. Some digging reveals that . Confusingly, Enoch seems to be.*

## Riemann Hypothesis/Biography of Riemann - Wikibooks

for every positive ε is equivalent to the Riemann hypothesis (). (For the meaning of these symbols, see .) The determinant of the order *n* is equal to *M*(*n*), so the Riemann hypothesis can also be stated as a condition on the growth of these determinants. The Riemann hypothesis puts a rather tight bound on the growth of *M*, since disproved the slightly stronger

## Riemann hypothesis - Wikipedia | Mathematics | …

The Riemann hypothesis is equivalent to many other conjectures about the rate of growth of other arithmetic functions aside from μ(*n*). A typical example is (), which states that if σ(*n*) is the , given by

## Riemann Hypothesis/The hypothesis - Wikibooks, …

Geoffrey Caveney, Jean-Louis Nicolas, and Jonathan Sondow. Robin’s theorem, primes, and a new elementary reformulation of the Riemann hypothesis. preprint arXiv:1110.5078, 2011.

## The Riemann Hypothesis For Dummies @ Things Of Interest

Another example was found by showing that the Riemann hypothesis is equivalent to a statement that the terms of the are fairly regular. More precisely, if *F*_{n} is the Farey sequence of order *n*, beginning with 1/*n* and up to 1/1, then the claim that for all ε > 0