#### One Citation

Ap\'ery limits for elliptic $L$-values

- Mathematics
- 2021

For an (irreducible) recurrence equation with coefficients from Z[n] and its two linearly independent rational solutions un, vn, the limit of un/vn as n → ∞, when exists, is called the Apéry limit.… Expand

#### References

SHOWING 1-10 OF 24 REFERENCES

Mahler’s Measure and the Dilogarithm (I)

- Mathematics
- Canadian Journal of Mathematics
- 2002

Abstract An explicit formula is derived for the logarithmic Mahler measure $m(P)$ of $P(x,\,y)\,=\,P(x)y-q(x)$ , where $p(x)$ and $q(x)$ are cyclotomic. This is used to find many examples of such… Expand

Ergodic theory for complex continued fractions

- Mathematics
- 1982

For a complex continued fraction algorithm the invariant measure for the shift transformation is determined explicitly in terms of elementary functions, and the transformation is shown to be ergodic.… Expand

On the arithmetic of crossratios and generalised Mertens' formulas

- Mathematics
- 2013

We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension up to… Expand

On measures of polynomials in several variables

- Mathematics
- 1981

The measure of a polynomial is defined as the exponential of a certain intractable-looking integral. However, it is shown how the measures of certain polynomials can be evaluated explicitly: when all… Expand

Mahler's Measure and Special Values of L-functions

- Mathematics, Computer Science
- Exp. Math.
- 1998

Some examples for which it appear that log M(P(x, y) = rL'(E, 0), where E is an elliptic curve and r is a rational number, often either an integer or the reciprocal of an integer. Expand

Well-poised generation of Apéry-like recursions

- Mathematics
- 2005

The idea to use classical hypergeometric series and, in particular, well-poised hypergeometric series in diophantine problems of the values of the polylogarithms has led to several novelties in… Expand

Apéry limits of differential equations of order 4 and 5.

- Mathematics
- 2008

The concept of Apery limit for second and third order differential equations is extended to fourth and fifth order equations, mainly of Calabi-Yau type. For those equations obtained from Hadamard… Expand

Diophantine approximation in the field Q(i(111/2))

- Mathematics
- 1978

Abstract In this paper, we consider the approximation spectrum w.r.t. the field Q ( i 2 ) . The smallest limit point of this spectrum is found to be c 0 = 1.78863819 … , where c 0 belongs to a real… Expand

A Third-Order Apéry-Like Recursion for ζ(5)

- Mathematics
- 2002

In 1978, Apery has given sequences of rational approximations to $\zeta(2)$ and $\zeta(3)$ yielding the irrationality of each of these numbers. One of the key ingredient of Apery's proof are… Expand

A FEW REMARKS ON LINEAR FORMS INVOLVING CATALAN'S CONSTANT

- Mathematics
- 2002

In the joint work (RZ) of T. Rivoal and the author, a hypergeometric construction was proposed for studing arithmetic properties of the values of Dirichlet's beta function �(s) at even positive… Expand