26 citations · 35 across the 6 of their papers we have counts for
17 papers · 1 filter
Prime Number Races
Andrew Granville, Greg Martin
This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of…
Constructions of Generalized Sidon Sets
Greg Martin, Kevin O'Bryant
We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k=s_1+s_2, s_i\in S; such sets are called Sidon sets if g=2 and…
Dimensions of the Spaces of Cusp Forms and Newforms on Gamma_0(N) and Gamma_1(N)
Greg Martin
A formula for the dimension of the space of cuspidal modular forms on of weight ( even) has been known for several decades. More recent but still well-known is…
Continuous Ramsey Theory and Sidon Sets
Greg Martin, Kevin O'Bryant
A symmetric subset of the reals is one that remains invariant under some reflection x --> c-x. Given 0 < x < 1, there exists a real number D(x) with the following property: if 0 <…
The Limiting Curve of Jarnik's Polygons
Greg Martin
In 1925, Jarnik defined a sequence of convex polygons for use in constructing curves containing many lattice points relative to their curvatures. Properly scaled, these polygons co…
The Unreasonable Effectualness of Continued Function Expansions
Greg Martin
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such gener…