27 citations · 236 across the 52 of their papers we have counts for
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An alternative representation of the Viète's formula for pi by Chebyshev polynomials of the first kind
S. M. Abrarov, B. M. Quine
There are several reformulations of the Viète's formula for pi that have been reported in the modern literature. In this paper we show another analog to the Viète's formula for pi…
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…
On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem
R. M. Abrarov, S. M. Abrarov
We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained results enable us to understan…
Regular and oscillatory parts for basic functions of prime numbers. I Regular parts
R. M. Abrarov, S. M. Abrarov
We consider the regular parts for basic functions of prime numbers with Riemann approximation accuracy.