Wyniki wyszukiwania

1

Dedekind cotangent sums

100%

Beck M.

Acta Arithmetica

|

2003

|

tom 109

|

nr 2

109-130

2

Rademacher-Carlitz polynomials

72%

Beck M., Kohl F.

Acta Arithmetica

|

2014

|

tom 163

|

nr 4

379-393

EN

We introduce and study the Rademacher-Carlitz polynomial $R(u,v,s,t,a,b) := ∑_{k=⌈s⌉}^{⌈s⌉+b-1} u^{⌊(ka+t)⌋}/b_{v^k}$ where $a,b ∈ ℤ_{>0}$, 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 $r_t(a,b) := ∑_{k=0}^{b-1} (((ka+t)/b)) ((k/b))$, 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 polynomials, we show how they are the only nontrivial ingredients of integer-point transforms $σ(x,y) := ∑_{(j,k)∈𝓟 ∩ ℤ²} x^jy^k$ of any rational polyhedron 𝓟, and we derive the reciprocity theorem for Dedekind-Rademacher sums as a corollary which follows naturally from our setup.

3

Bernoulli-Dedekind sums

72%

Beck M., Chavez A.

Acta Arithmetica

|

2011

|

tom 149

|

nr 1

65-82

Ograniczanie wyników

3 Acta Arithmetica

3 Beck M.

1 Chavez A.

1 Kohl F.

1 2014

1 2011

1 2003

Dedekind cotangent sums

Rademacher-Carlitz polynomials

Bernoulli-Dedekind sums