О мере иррациональности числа $\pi$@@@On the irrationality measure of $\pi$

  title={О мере иррациональности числа \$\pi\$@@@On the irrationality measure of \$\pi\$},
  author={Владислав Хасанович Салихов and Vladislav Khasanovich Salikhov},
13 Citations
Möbius formulas for densities of sets of prime ideals
We generalize results of Alladi, Dawsey, and Sweeting and Woo for Chebotarev densities to general densities of sets of primes. We show that if K is a number field and S is any set of prime idealsExpand
On Irrationality Measure of arctan $$\frac{1}{3}$$13
We investigate the arithmetic properties of the value arctan $$\frac{1}{3}$$13. We elaborate special integral construction with the property of symmetry for evaluating irrationality measure of thisExpand
The irrationality measure of π is at most 7.103205334137…
We use a variant of Salikhov's ingenious proof that the irrationality measure of $\pi$ is at most $7.606308\dots$ to prove that, in fact, it is at most $7.103205334137\dots$. Accompanying MapleExpand
Directional Poincaré inequalities along mixing flows
We provide a refinement of the Poincaré inequality on the torus Td$\mathbb{T}^{d}$: there exists a set B⊂Td$\mathcal{B} \subset \mathbb{T} ^{d}$ of directions such that for every α∈B$\alpha \inExpand
Comparing a series to an integral
0 u x e u du, where x is a real parameter, and the approximating sum P 1D1 k x e k . We use properties of Bernoulli numbers to show that this difference is unbounded and has infinitely many zeros. WeExpand
On the irrationality measure of
Hermite-Padé Rational Approximation to Irrational Numbers
We will describe a method for proving that a given real number is irrational. It amounts to constructing explicit rational approximants to the real number which are “better than possible” should theExpand
On the irrationality exponent of the number ln 2
We propose another method of deriving the Marcovecchio estimate for the irrationality measure of the number ln 2 following, for the most part, the method of proof of the irrationality of the numberExpand


A Lower Bound for Rational Approximations to π
Abstract We give a sharp lower bound for rational approximations to π by modifying the classical approximation formula to the system {(log(1 − x )) j } 1 ≤ j ≤ K due to Hermite. In fact, it will heExpand
Infinite component two-dimensional completely integrable systems of KdV type
We investigate the infinite-dimensional generalization of the non-linear Schrodinger equation. We consider both non-stationary and stationary subsystems. The close one-to-one connection with theExpand