149 citations · 319 across the 56 of their papers we have counts for
5 papers · 1 filter
-adic quotient sets II: quadratic forms
Christopher Donnay, Stephan Ramon Garcia, Jeremy Rouse
For , we consider . If is the set of nonzero values assumed by a quadratic form, when is dense in the -adic…
The Bateman-Horn Conjecture: Heuristics, History, and Applications
Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, Stephan Ramon Garcia
The Bateman-Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green-T…
An improved uncertainty principle for functions with symmetry
Stephan Ramon Garcia, Gizem Karaali, Daniel J. Katz
Chebotarëv proved that every minor of a discrete Fourier matrix of prime order is nonzero. We prove a generalization of this result that includes analogues for discrete cosine and…
Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums
Stephan Ramon Garcia, George Todd
We connect the sixth power moment of Kloosterman sums to elliptic curves. This yields an elementary proof that with are .
Factorization length distribution for affine semigroups I: numerical semigroups with three generators
Stephan Ramon Garcia, Christopher O'Neill, Samuel Yih
Most factorization invariants in the literature extract extremal factorization behavior, such as the maximum and minimum factorization lengths. Invariants of intermediate size, suc…