#### 13 Citations

Möbius formulas for densities of sets of prime ideals

- Mathematics
- 2019

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 ideals… Expand

On Irrationality Measure of arctan $$\frac{1}{3}$$13

- Mathematics
- 2019

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 this… Expand

The irrationality measure of π is at most
7.103205334137…

- Mathematics
- 2019

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 Maple… Expand

Directional Poincaré inequalities along mixing flows

- Mathematics
- 2015

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 \in… Expand

Comparing a series to an integral

- Mathematics
- 2014

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. We… Expand

Hermite-Padé Rational Approximation to Irrational Numbers

- Mathematics
- 2011

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 the… Expand

On the irrationality exponent of the number ln 2

- Mathematics
- 2010

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 number… Expand

#### References

SHOWING 1-4 OF 4 REFERENCES

A Lower Bound for Rational Approximations to π

- Mathematics
- 1993

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 he… Expand

Infinite component two-dimensional completely integrable systems of KdV type

- Physics
- 1982

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 the… Expand