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Primes in almost all short intervals and the distribution of the zeros of the Riemann zeta-function
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zaccagnini, Alessandro |
| Copyright Year | 2007 |
| Abstract | Abstract We study the relations between the distribution of the zeros of the Riemann zeta-function and the distribution of primes in “almost all” short intervals. It is well known that a relation like ψ(x)−ψ(x−y) ∼ y holds for almost all x ∈ [N, 2N ] in a range for y that depends on the width of the available zero-free regions for the Riemann zeta-function, and also on the strength of density bounds for the zeros themselves. We also study implications in the opposite direction: assuming that an asymptotic formula like the above is valid for almost all x in a given range of values for y, we find zero-free regions or density bounds. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://people.math.unipr.it/alessandro.zaccagnini/psfiles/papers/Q429.pdf |
| Alternate Webpage(s) | http://www.math.unipr.it/~zaccagni/psfiles/papers/Q429.pdf |
| Alternate Webpage(s) | http://people.dmi.unipr.it/alessandro.zaccagnini/psfiles/papers/Q429.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |