In this article we will study the spectral properties of a deterministic signal exponentially damped in the past and in the future (the damping in the future is controlled by a time constant). The ...
The Riemann hypothesis raised in 1859 is one of the six unsolved Millennium problems, and its proof will greatly facilitate the understanding of the distribution laws of prime numbers. For a long time ...
The Riemann zeta function, a central object in analytic number theory, has long intrigued mathematicians and physicists alike. Its non-trivial zeros not only encapsulate the distribution of prime ...
This is a preview. Log in through your library . Abstract Assuming the Riemann Hypothesis, we prove that a positive proportion of the time, the gap between consecutive zeros of the Riemann ...
The Millennium Prize Problems, announced in 2000 by the Clay Mathematics Institute in the United States, are problems with a prize of $1 million (approximately 160 million yen). One of these problems ...
Over the past few days, the mathematics world has been abuzz over the news that Sir Michael Atiyah, the famous Fields Medalist and Abel Prize winner, claims to have solved the Riemann hypothesis. If ...
If two physicists are right, a single electron might know more about numbers than all of the world’s mathematicians. In an upcoming Physical Review Letters, the researchers hint that the dynamics of ...
Prime numbers, the indivisible atoms of arithmetic, seem to be strewn haphazardly along the number line, starting with 2, 3, 5, 7, 11, 13, 17 and continuing without pattern ad infinitum. But in 1859, ...
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