9 citations · 24 across the 11 of their papers we have counts for
11 papers
Properties and applications of the prime detecting function: infinitude of twin primes, asymptotic law of distribution of prime pairs differing by an even number
R. M. Abrarov, S. M. Abrarov
The prime detecting function (PDF) approach can be effective instrument in the investigation of numbers. The PDF is constructed by recurrence sequence - each successive prime adds…
Sieve Procedure for the Möbius prime-functions, the Infinitude of Primes and the Prime Number Theorem
R. M. Abrarov, S. M. Abrarov
Using a sieve procedure akin to the sieve of Eratosthenes we show how for each prime to build the corresponding Möbius prime-function, which in the limit of infinitely large pr…
Probabilistic interpretation of the Möbius function identity and the Riemann Hypothesis
R. M. Abrarov, S. M. Abrarov
We obtained the probabilities for the values of the Möbius function for arbitrary numbers and found that the asymptotic densities of the squarefree integers among the odd and even…
Mode coupling and evolution in broken-symmetry plasmas
E. Ya. Sherman, R. M. Abrarov, J. E. Sipe
The control of nonlinear processes and possible transitions to chaos in systems of interacting particles is a fundamental physical problem. We propose a new nonuniform solid-state…
Formulas for Positive, Negative and Zero Values of the Möbius Function
R. M. Abrarov, S. M. Abrarov
We obtained the formulas for the quantities of positive, negative and zero values of the Mobius function for any real x in terms of the Mobius function values for square root of x…
Riemann Hypothesis may be proved by induction
R. M. Abrarov, S. M. Abrarov
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expres…