Related papers: Much ado about Zero
We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to areas related to partial sums of powers. We apply these…
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
Some mathematical properties of the Erd\"os number and its formal equivalents are shown. An informetric equivalent is presented: the Rousseau number. This contribution honors Ronald Rousseau for his 73th birthday.
I give some claims on primorial prime numbers for interested readers in number theory.
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate
We give an elementary proof of a result which is not as well known as it should be: a ring with a specified finite number of zero divisors is finite, with a precise bound on its order.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
Basic arithmetic is the cornerstone of mathematics and computer sciences. In arithmetic, 'division by zero' is an undefined operation and any attempt at extending logic for algebraic division to incorporate division by zero has resulted in…
What would you do if you were asked to "add" knowledge? Would you say that "one plus one knowledge" is two "knowledges"? Less than that? More? Or something in between? Adding knowledge sounds strange, but it brings to the forefront…
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
We discuss several aspects of infinity in the history of mathematics.
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
New numbers, called Guinness numbers, are introduced using certain function of natural argument. Few problems related to these numbers are formulated.
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
We will give a simple proof of the ambiguous class number formula.
Summing the values of the real portion of the logarithmic integral of n^rho, where rho is one of a consecutive series of zeros of the Riemann zeta function, reveals an unexpected periodicity to the sum. This is the cycle problem.
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.