Related papers: The Ambiguous Class Number Formula Revisited

This version is a significant improvement of the original paper. It includes a new section where we discuss norm tori in some detail. The new abstract is the following: In this paper we obtain Chevalley's ambiguous class number formula for…

A "simple trace formula" is used to derive an asymptotic result for class numbers of complex cubic orders.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We present a simple inductive proof of the Lagrange Inversion Formula.

We give an asymptotic formula for class numbers of orders in cubic number fields.

In this note we remark that Chevalley's ambiguous class number formula is an immediate consequence of the Hasse norm theorem, the local and global norm index theorems for cyclic extensions.

We present a new, elementary, dynamical proof of the prime number theorem.

We present a new variant of the Faa di Bruno formula with a simpler summation order.

We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we…

It is shown that the class number for negative discriminant $D$ can be expressed in terms of the base $B$ expansions of reduced fractions $\frac{x}{|D|}$, where $B$ is an integer prime to $D$. This result is then formulated to obtain…

We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.

A renormalizable ambiguity-free formulation of the Higgs-Kibble model is proposed.

We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree $2q$, where $q$ is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units…

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

We give a new recurrent inequality on a class of vertex Folkman numbers.

A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.

We give a new proof of Lucas' Theorem in elementary number theory.

The derivation of the quantum retrodictive probability formula involves an error, an ambiguity. The end result is correct because this error appears twice, in such a way as to cancel itself. In addition, however, the usual expression for…

We survey the classical results on the prime number theorem

In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.