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Let Re(s)﹦π(n)/n,(n﹦2), and Im(s)﹦((π(n)﹣π(2))㏒n)i,(n>2), Riemann hypothesis is proved.
σ﹢ti is irrelevant to the distributive law of primes.
We consider integral and series transformations, which are associated with Ramanujan's identities, involving various arithmetic functions and a ratio of products of Riemann's zeta functions of differe...
Nicolas criterion for the Riemann Hypothesis is based on an inequality that Euler totient function must satisfy at primorial numbers. A natural approach to derive this inequality would be to prove tha...
We present a brief review of the spectral approach to the Riemann hypothesis,according to which the imaginary part of the non trivial zeros of the zeta function are the the eigenvalues of the Hamilton...
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral

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