41 citations · 66 across the 22 of their papers we have counts for
7 papers · 1 filter
A Note on Counting Lattice Points in Bounded Domains
J. LaChapelle
Zeros and poles of -tuple zeta functions, that are defined here implicitly, enable localization onto prime-power -tuples in pair-wise coprime -lattices . A…
Exact Summatory Functions for Prime -tuples
J. LaChapelle
Exact summatory functions that count the number of prime -tuples up to some cut-off integer are presented. Related -tuple analogs of the first and second Chebyshev functions…
On the infinitude of Prime -tuples
J. LaChapelle
Starting with Zhang's theorem on the infinitude of prime doubles, we give an inductive argument that there exists an infinite number of prime -tuples for at least one admissible…
A Gamma Distribution Hypothesis for Prime -tuples
J. LaChapelle
We conjecture average counting functions for prime -tuples based on a gamma distribution hypothesis for prime powers. The conjecture is closely related to the Hardy-Littlewood c…
Functional Mellin and Zeta Zeros
J. LaChapelle
A key theorem formulated in the context of functional Mellin transforms generalizes the important relationship . Along with the involution symmetry of…
Evidence of a Gamma Distribution for Prime Powers
J. LaChapelle
If the prime numbers are pseudo-randomly distributed, then analogy with quantum systems suggests that counting primes might be modeled by a non-homogeneous Poisson process. Consequ…