Related papers: The Ambiguous Class Number Formula Revisited
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
We prove a curious identity for the Bernoulli numbers.
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
We derive an analytic class number formula valid for an order in a product of $S$-integers in global fields, or equivalently for reduced finite-type affine schemes of pure dimension $1$ over $\mathbb{Z}$.
Coping with ambiguity has recently received a lot of attention in natural language processing. Most work focuses on the semantic representation of ambiguous expressions. In this paper we complement this work in two ways. First, we provide…
We provide a short proof of the 1-dimensional flat chain conjecture.
We present in this work a new and simple proof of the false centre theorem.
We provide a simple proof of Kamp's theorem.
In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
We provide a new characterization of the logarithmic Sobolev inequality.
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…
Bernoulli numbers are usually expressed in terms of their lower index numbers (recursive). This paper gives an explicit formula for Bernoulli numbers of even index. The formula contains a remarkable sequence of determinants.
We give a new simpler proof of a theorem of Jayne and Rogers.
We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime $p$, each side of Darmon's conjectured formula (indexed by positive integers $n$) is "almost" a…
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…
We obtain simple proofs of certain inequalites for bivariate means.
We give a presentation of abelian class field theory.
An error in the proof of Bell's Theorem is identified and a semiclassical model of the EPRB experiment is presented