3 citations · 3 across the 5 of their papers we have counts for
15 papers
Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups
Stephan Ramon Garcia, Christopher O'Neill, Gabe Udell
For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factoriza…
A Gallery of Gaussian Periods
Ellen Eischen, Stephan Ramon Garcia
Gaussian periods are certain sums of roots of unity whose study dates back to Gauss's seminal work in algebra and number theory. Recently, large scale plots of Gaussian periods hav…
An effective analytic formula for the number of distinct irreducible factors of a polynomial
Stephan Ramon Garcia, Ethan Simpson Lee, Josh Suh +1
We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors of a polynomial . We use an explicit version o…
Explicit Mertens' Theorems for Number Fields
Stephan Ramon Garcia, Ethan Simpson Lee
Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.
Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators
Stephan Ramon Garcia, Mohamed Omar, Christopher O'Neill +1
For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrar…
Multidimensional Schinzel-type theorems for multiplicative functions near prime tuples
Stephan Ramon Garcia, Gabe Udell, Jiahui Yu
Assuming Dickson's conjecture, we obtain multidimensional analogues of recent results on the behavior of certain multiplicative arithmetic functions near twin-prime arguments. This…