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4 papers · 1 filter
An average of generalized Dedekind sums
Travis Dillon, Stephanie Gaston
We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By ca…
Differences of Harmonic Numbers and the -Conjecture
Natalia da Silva, Serban Raianu, Hector Salgado
Our main source of inspiration was a talk by Hendrik Lenstra on harmonic numbers, which are numbers whose only prime factors are two or three. Gersonides proved 675 years ago that…
Applications of differential algebra to algebraic independence of arithmetic functions
Wai Yan Pong
We generalize and unify the proofs of several results on algebraic in- dependence of arithmetic functions and Dirichlet series by a theorem of Ax on differential Schanuel conjectur…
Length Spectra of Natural Numbers
Wai Yan Pong
Two numbers are spectral equivalent if they have the same length spectrum. We show how to compute the equivalence classes of this relation. Moreover, we show that these classes can…