7 papers · 1 filter
Conditions for solving polynomial equations using algebraic and hypergeometric functions
Nikos Mantzakouras, Carlos López Zapata, Nid Na Ratch
In this paper, we focus on clarifying the concept of solving equations of degree greater than six using continuous functions or hypergeometric functions and providing another proof…
Holder continuity of an alternating Erdos series on prime K-tuples
Nikos Mantzakouras
This open problem, first posed by Erdοs, was further explored by Terence Tao. Tao work shows that the series can converge conditionally, but only under a sufficiently strong form o…
Diophantine FLINT-HILLS series
Nikos Mantzakouras, Carlos López Zapata
We prove the convergence of the FLINT-HILLS series and establish new criteria for a similar type of diophantine or lacunary series, which faces issues due to spaced long terms comi…
Generalized solutions of Polynomial and Transcendental Equations by the strong method of (Generalized Iterative Method approximation of Roots (GRIM) )
Nikos Mantzakouras, Eteri Biragova
In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach sp…
Unconditional representations of the Euler-Mascheroni constant and the Bernoulli numbers via the Taylor coefficients of the Riemann ξ-function, and a hierarchy of exact relations at the central point
Nikos Mantzakouras, Carlos López
We give a self-contained, numerically verified derivation of three equivalent unconditional representations of the Euler--Mascheroni constant as a rapidly convergent series in…
Hypothesis of Riemann is rejected by definition
Nikos Mantzakouras
Hypothesis of Riemann is rejected by definition, because ζ(s), where s zeros of ζ(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/…
Solve Polynomial and transcendental Equations with use Generalized Theorem (Method Lagrange)
Nikos Mantzakouras
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the…