A closer look at lattice points in rational simplices.
Six little squares and how their numbers grow.
The polynomial part of a restricted partition function related to the Frobenius problem.
Some experimental results on the Frobenius problem.
Dedekind cotangent sums
Bernoulli-Dedekind sums
Rademacher-Carlitz polynomials
We introduce and study the Rademacher-Carlitz polynomial where , s,t ∈ ℝ, and u and v are variables. These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view R(u,v,s,t,a,b) as a polynomial analogue (in the sense of Carlitz) of the Dedekind-Rademacher sum , which appears in various number-theoretic, combinatorial, geometric, and computational contexts. Our results come in three flavors: we prove a reciprocity theorem for Rademacher-Carlitz...
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