Related papers: The Ambiguous Class Number Formula Revisited
We show how, starting from the Tate exact sequence for units of Ritter and Weiss, one can obtain an algebraic proof of Brauer's class number formula, using the formalism of regulator constants.
In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…
In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versions of each theorems are also presented.
Gap balancing numbers are a certain generalization of balancing and cobalancing numbers that arise from studying the equation ${T(L)+T(B)=T(m)}$ where $T(i)$ is the $i$th triangular number. In this paper, we survey early results, attempt to…
We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.
We prove a binomial formula for Macdonald polynomials and consider applications of it.
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
In this paper, we give a simple counter example to the famous Hodge conjecture.
Ambiguity is shown in the context of the differential calculus of several variables and with the help of the language of category theory, a way to solve it in its most general form is offered. It is also shown that this new definition is…
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
Let $F$ be a number field and $\mathcal{O}_F$ its ring of integers. We use Chevalley's ambiguous class number formula to give a criterion for the non-existence of solutions to the unit equation $\lambda + \mu = 1$, $\lambda, \mu \in…
We review Andr\'e Luiz Barbosa's paper "P != NP Proof," in which the classes P and NP are generalized and claimed to be proven separate. We highlight inherent ambiguities in Barbosa's definitions, and show that attempts to resolve this…
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We prove the Aharoni Berger Conjecture
We claim to resolve the P=?NP problem via a formal argument for P=NP.
We are interested in formulas for the number of elements in certain classes of numerical semigroups