Related papers: Irrationality Measure Of $\pi^2$
The longstanding discrepancy between the measured and the predicted values of the anomalous magnetic moment of the muon, $a_\mu = (g-2)/2$, is one of the most intriguing potential hints of new physics in particle physics. After a brief…
The muon g-2 experiment at Brookhaven National Laboratory measures the anomalous magnetic moment of the muon, $a_\mu$, very precisely. This measurement tests the Standard Model. The analysis for the data collected in 2000 (a $\mu^+$ run) is…
A precise measurement of the anomalous g value, a_mu=(g-2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron. The result a_mu^+=11 659 202(14)(6) X 10^{-10} (1.3 ppm) is in good agreement with…
Given an irrational number $\alpha$ consider its irrationality measure function $\psi_{\alpha}(t)=\min\limits_{1\le q\le t, q\in\mathbb{Z}}\|q\alpha\|$. The set of all values of $\lambda(\alpha)=(\limsup\limits_{t\to\infty}…
In this paper we study the property of normality of a number in base 2. A simple rule that associates a vector to a number is presented and the property of normality is stated for the vector associated to the number. The problem of testing…
We show that, on the Riemann hypothesis, $\limsup_{X\to\infty}I(X)/X^{2} \leq 0.8603$, where $I(X) = \int_X^{2X} (\psi(x)-x)^2\,dx.$ This proves (and improves on) a claim by Pintz from 1982. We also show unconditionally that…
We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying "permutation group" structures. Our principal arithmetic achievement…
The degree of irrationality of a smooth projective variety $X$ is the minimal degree of a dominant rational map $X\dashrightarrow \mathbb{P}^{\dim X}$. We show that if an abelian surface $A$ over $\mathbb{C}$ is such that the image of the…
We compute the exact irrationality exponents of certain series of rational numbers, first studied in a special case by Hone, by transforming them into suitable continued fractions.
To prove by probabilistic methods that every $(n-1)$-dimensional section of the unit cube in $R^n$ has volume at most $\sqrt 2$, K. Ball made essential use of the inequality $$ \frac{1}{\pi}\int_{-\infty}^{\infty} \left(\frac{\sin^2…
The Muon (g-2) Experiment (E821) at Brookhaven National Laboratory (BNL) has measured the anomalous magnetic moment of the positive muon to an unprecedented precision of 1.3 parts per million. The result, a_{\mu^+} = (g-2)/2 = 11 659…
The degree of irrationality of a projective variety $X$ is defined to be the smallest degree rational dominant map to a projective space of the same dimension. For abelian surfaces, Yoshihara computed this invariant in specific cases, while…
We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary…
The normality measure $\mathcal{N}$ has been introduced by Mauduit and S{\'a}rk{\"o}zy in order to describe the pseudorandomness properties of finite binary sequences. Alon, Kohayakawa, Mauduit, Moreira and R{\"o}dl proved that the minimal…
A new measurement of the branching ratio, $R_{e/\mu} =\Gamma (\pi^+ \rightarrow \mbox{e}^+ \nu + \pi^+ \rightarrow \mbox{e}^+ \nu \gamma)/ \Gamma (\pi^+ \rightarrow \mu^+ \nu + \pi^+ \rightarrow \mu^+ \nu \gamma)$, resulted in…
The Muon g-2 collaboration has measured the anomalous magnetic g value, a = (g-2)/2, of the positive muon with an unprecedented uncertainty of 0.7 parts per million. The result, based on data collected in the year 2000 at Brookhaven…
The muon (g-2) experiment at BNL has completed four data runs for the positive muon, beginning in 1997 and has just finished its first run for the negative muon. Recently the analysis of a 1.3 ppm result based on the 1999 run was completed…
A new experiment to measure the muon g-2 factor is proposed. We suppose the sensitivity of this experiment to be about 0.03 ppm. The developed experiment can be performed on an ordinary storage ring with a noncontinuous field created by…
This work is motivated by a paper of Davenport and Schmidt, which treats the question of when Dirichlet's theorems on the rational approximation of one or of two irrationals can be improved and if so, by how much. We consider a…
Refining an argument of the second author, we improve the known bounds for the number of rational points near a submanifold of $\mathbb{R}^d$ of intermediate dimension under a natural curvature condition. Furthermore, in the codimension $2$…