Corpus ID: 237940799

Ap\'ery limits and Mahler measures

  title={Ap\'ery limits and Mahler measures},
  author={Wadim Zudilin},
It is the first paper which relates Apéry limits to Mahler measures. 
Ap\'ery limits for elliptic $L$-values
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


Mahler’s Measure and the Dilogarithm (I)
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 suchExpand
Ergodic theory for complex continued fractions
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
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 toExpand
On measures of polynomials in several variables
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 allExpand
Mahler's Measure and Special Values of L-functions
  • D. W. Boyd
  • 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
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 inExpand
Apéry limits of differential equations of order 4 and 5.
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 HadamardExpand
Diophantine approximation in the field Q(i(111/2))
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 realExpand
A Third-Order Apéry-Like Recursion for ζ(5)
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 areExpand
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 positiveExpand