The pair correlation of zeros of the Riemann zeta function and distribution of primes
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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One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...
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In 1972 Montgomery [20, 21] introduced a new method for studying the zeros of the Riemann zeta-function. One of his main accomplishments was to determine partially the pair correlation of zeros, and to apply his results to obtain new information on multiplicity of zeros and gaps between zeros. Perhaps more importantly, he conjectured on number-theoretic grounds an asymptotic formula for the pai...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2001
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s000130050540