1 citations · 3 across the 7 of their papers we have counts for
8 papers
Fourier Series in Fractional Dimensional Space
Ali Dorostkar, Ahmad Sabihi
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function . We call it fractional Fourier series of the order .…
On optimization and solution of roots of a function using Taylor's expansion and fractional derivatives
Ali Dorostkar, Ahmad Sabihi
A method is given for finding roots of a one-variable function using Taylor's expansion of that function and fractional derivative calculated at a suitable tangent point without us…
A Novel Method for Drawing a Circle Tangent to Three Circles Lying on a Plane by Straightedge,Compass,and Inversion Circles
Ahmad Sabihi
In this paper, we present a novel method to draw a circle tangent to three given circles lying on a plane. Using the analytic geometry and inversion (reflection) theorems, the cent…
An analytical proof for Lehmer's totient conjecture using Mertens' theorems
Ahmad Sabihi
We make an analytical proof for Lehmer's totient conjecture. Lehmer conjectured that there is no solution for the congruence equation with composite intege…
An approach towards the proof of the strong Goldbach's conjecture for sufficiently large even integers
Ahmad Sabihi
We approach a new proof of the strong Goldbach's conjecture for sufficiently large even integers by applying the Dirichlet's series. Using the Perron formula and the Residue Theore…
Robin's inequality,Lagarias' criterion, and Riemann hypothesis
Ahmad Sabihi
In this paper, we make use of Robin and Lagarias' criteria to prove Riemann hypothesis. The goal is, using Lagarias criterion for since Lagarias criterion states that Rie…
On solutions of some of unsolved problems in number theory, specifically on the distribution of primes
Ahmad Sabihi
We solve some famous conjectures on the distribution of primes. These conjectures are to be listed as Legendre's, Andrica's, Oppermann's, Brocard's, Cramér's, Shanks', and five Sma…
On the Firoozbakht's conjecture
Ahmad Sabihi
This paper proves Firoozbakht's conjecture using Rosser and Schoenfelds' inequality on the distribution of primes. This inequality is valid for all natural numbers . Fi…