Pair correlation estimates for the zeros of the zeta function via semidefinite programming
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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In this paper, we study a more general pair correlation function, F h (x, T), of the zeros of the Riemann zeta function. It provides information on the distribution of larger differences between the zeros.
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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: Advances in Mathematics
سال: 2020
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.106926