#### 32 Citations

Square exponent of irrationality of ln2

- Mathematics
- 2012

A new proof of the theorem on the non-quadraticity measure ln 2 is given in the paper.

Approximation of values of the Gauss hypergeometric function by rational fractions

- Mathematics
- 2010

AbstractWe consider a new approach to estimating the irrationality measure of numbers that are values of the Gauss hypergeometric function. Some of the previous results are improved, in particular,… 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

Hypergeometric rational approximations to ζ(4)

- Mathematics
- Proceedings of the Edinburgh Mathematical Society
- 2020

Abstract We give a new hypergeometric construction of rational approximations to ζ(4), which absorbs the earlier one from 2003 based on Bailey's 9F8 hypergeometric integrals. With the novel… Expand

Automatic discovery of irrationality proofs and irrationality measures

- Mathematics
- 2019

We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes… 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

Hypergeometry inspired by irrationality questions

- Mathematics
- 2018

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'… Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Austria E-mail: marcovr8@univie.ac.at Received on 1.12

- 2008

Diophantine approximations of log 2 and other logarithms

- Mathematics
- 2008

We describe a new approach to estimating μ(log 2), without improving Rukhadze’s result (1987). We find estimates for approximations to the number log 2 by numbers from the field ℚ(√2), to the number… Expand

The permutation group method for the dilogarithm

- Mathematics
- 2005

We give qualitative and quantitative improvements on all the best pre- viously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying our… Expand

Approximation measures for logarithms of algebraic numbers

- Mathematics
- 2001

Given a number field K and a number ) lll we say that A > 0 is a
K-irrationality measure of 03BE if, for any e > 0, > - ( 1 + e) p h(o)
for all p E K with sufficiently large Weil logarithmic height… Expand

Irrationalité d’une infinité de valeurs de la fonction zêta aux entiers impairs

- Mathematics
- 2001

Au contraire des nombres ζ(2n)=∑k≥1 1/k2n= (−1)n−122n−1 B2nπ2n/(2n)! (n ≥ 1), dont la transcendance est une conséquence de celle de π, peu de résultats sont actuellement connus sur la nature… Expand

Hypergeometric functions and irrationality measures

- in: Analytic Number Theory (Kyoto,
- 1996

On irrationality measures of the values of Gauss hypergeometric function

- Mathematics
- 1993

The paper gives irrationality measures for the values of some Gauss hypergeometric functions both in the archimedean andp-adic case. Further, an improvement of general results is obtained in the case… Expand