1 citations · 2 across the 31 of their papers we have counts for
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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…