Gaps between primes, and the pair correlation of zeros of the zeta-function
نویسندگان
چکیده
منابع مشابه
The pair correlation of zeros of the Riemann zeta function and distribution of primes
Assuming a special version of the Montgomery-Odlyzko law on the pair correlation of zeros of the Riemann zeta function conjectured by Rudnick and Sarnak and assuming the Riemann Hypothesis, we prove new results on the prime number theorem, difference of consecutive primes, and the twin prime conjecture. 1. Introduction. Assuming the Riemann Hypothesis (RH), let us denote by 1=2 ig a nontrivi...
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15 صفحه اولLarge Gaps between the Zeros of the Riemann Zeta Function
If the Riemann hypothesis (RH) is true then the non-trivial zeros of the Riemann zeta function, ζ(s), satisfy 1/2+iγn with γn ∈ R. Riemann noted that the argument principle implies that number of zeros of ζ(s) in the box with vertices 0, 1, 1 + iT, and iT is N(T ) ∼ (T/2π) log (T/2πe). This implies that on average (γn+1 − γn) ≈ 2π/ log γn and hence the average spacing of the sequence γ̂n = γn lo...
متن کاملGaps between consecutive zeros of the Riemann zeta-function
An important problem in number theory is to study the distribution of the non-trivial zeros of the Riemann zeta-function which, if one is willing to assume the Riemann Hypothesis, all lie on a vertical line. It is relatively easy to count how many of these zeros lie in a large interval, so the average spacing between consecutive zeros is easy to compute. However, it is a difficult and interesti...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1982
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-41-1-85-99