More precise Pair Correlation Conjecture on the zeros of the Riemann zeta function
نویسندگان
چکیده
منابع مشابه
More precise Pair Correlation Conjecture
In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.
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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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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...
متن کاملPair Correlation of the zeros of the Riemann zeta function in longer ranges
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.
متن کاملSimple Zeros of the Riemann Zeta-function
Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2004
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa114-3-1