1 citations · 2 across the 31 of their papers we have counts for
37 papers
Complex Circles of Partition and the Expansion Principles
Berndt Gensel, Theophilus Agama
In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, exten…
An inequality of multiple integral of norm of vectors in
Theophilus Agama
In this paper, we prove some new inequalities. To facilitate this proof, we introduce the notion of the local product on a sheet and associated space.
On the flint hills series
Theophilus Agama
In this note, we study the flint hills series of the form \begin{align} \sum \limits_{n=1}^{\infty}\frac{1}{(\sin^2n) n^3}\nonumber \end{align} via a certain method. The method ess…
On addition chains and progress on the Scholz conjecture
Theophilus Agama
In this paper, we develop some new classes of methods to study the Scholz conjecture on addition chains. It turns out that the exponents of numbers of the form largely dete…
A new proof of some matrix inequalities
Theophilus Agama
In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{…
On the general no-three-in-line problem
Theophilus Agama
In this paper, we show that the number of points that can be placed in the grid for all with so that no…
On the Gap sequence and the Gilbreath conjecture
Theophilus Agama
Motivated by the Gilbreath conjecture, we develop the notion of the gap sequence induced by any sequence of numbers. We introduce the notion of the path and associated circuits ind…
Simple close curve magnetization and application to Bellman's lost in the forest problem
Theophilus Agama
In this paper, we introduce and develop the notion of simple closed-curve magnetization. We provide an application to the Bellman lost in the forest problem by assuming special geo…
Studies in Additive Number Theory by Circles of Partition
Theophilus Agama, Berndt Gensel
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partit…
Multivariate expansivity theory and Pierce-Birkhoff conjecture
Theophilus Agama
Motivated by the Pierce-Birkhoff conjecture, we launch an extension program for single variable expansivity theory. We study this notion under tuples of polynomials in the ring $\m…
On the Erdős-Turán additive base conjecture
Theophilus Agama
In this paper, we formulate and prove several variants of the Erdős-Turán additive bases conjecture.
Ulam numbers have zero density
Theophilus Agama
In this paper, we show that the natural density of Ulam numbers satisfies . That is, we show that for \begin…
New bounds for the Heilbronn triangle problem
Theophilus Agama
Using ideas from the geometry of compression, we improve on the current upper and lower bounds of the Heilbronn triangle problem. In particular, let denote the minimal area…
On the pointwise periodicity of multiplicative and additive functions
Theophilus Agama
We study the problem of estimating the number of points of coincidences of an idealized gap on the set of integers under a given multiplicative function $g:\mathbb{N}\longrightarro…
On the distribution of addition chains
Theophilus Agama
Addition chains are a classical construction for fast exponentiation and related computation problems. In this paper, we study a chain for a fixed integer by decomposing each g…
The spanning method and the Lehmer totient problem
Theophilus Agama
In this paper, we introduce and develop the notion of spanning of integers along functions . We apply this method to a class of problems tha…
On the Erdős distance problem
Theophilus Agama
In this paper, using the compression method, we recover the lower bound for the Erdős unit distance problem and provide an alternative proof to the distinct distance conjecture. In…
The prime pairs are equidistributed among the coset lattice congruence classes
Theophilus Agama, Marco Bortolamasim, Arturo Tapia
In this paper we show that for some constant and for any there exist some such that, If then we have \begin{align} Ψ_z(x;\mathcal{N}_q(a,b…
The Compression method and applications
Theophilus Agama
In this paper, we introduce and develop the method of compression of points in space. We introduce the notion of the mass, the rank, the entropy, the cover and the energy of compre…
The theory of the Collatz process and the method of dynamical balls
Theophilus Agama
In this paper, we introduce and develop the theory of the Collatz process and the method of dynamical balls. We leverage this theory to study the Collatz conjecture. This theory al…
Distribution of boundary points of expansion and application to the lonely runner conjecture
Theophilus Agama
In this paper, we study the distribution of the boundary points of expansion. As an application, we say something about the lonely runner problem. We show that given runners $\…
Expansivity theory and Sendov's conjecture
Theophilus Agama
In this paper we introduce and develop the concept of expansivity of a tuple whose entries are elements from the polynomial ring . As an inverse problem, we examine…
The prime index function
Theophilus Agama
In this paper we introduce the prime index function \begin{align}ι(n)=(-1)^{π(n)},\nonumber \end{align} where is the prime counting function. We study some elementary proper…
The Theory of ramification
Theophilus Agama
In this paper, we introduce and develop the concept of \emph{ramification} in a given modulus. We study some properties in relation to this concept and it's connection to some impo…