On $ζ(2n)$. Even simpler
We solve an interpolation problem for computing $ζ(2n)$ in a rather elementary way, by generalizing the main idea in \cite{SE}.
math.NT↗
arXiv subjects
Samuel G. Moreno
Publications and source records attributed to Samuel G. Moreno.
A Short Proof of a Concrete Sum
We give an alternative proof of a formula that generalizes Hermite's identity. Instead involving modular arithmetic, our short proof relies on the Fourier-type expansion for the floor function and on a trigonometric formula.
math.NT↗
A One-Sentence and Truly Elementary Proof of the Basel Problem
By doing a slight change to a beautiful and widely unknown argument by E. L. Stark [E. L. Stark, Application of a Mean Value Theorem for Integrals to Series Summation, Amer. Math. Monthly 85 (1978) 481--483.] we get a candidate to be considered as one of the shortest and most elementary proofs of the celebrated Basel Problem. Furthermore, we give a comprehensive list of references on this topic, displayed in chronological order from Euler to present.
math.HO↗