Corpus ID: 237940799

Ap\'ery limits and Mahler measures

@inproceedings{Zudilin2021AperyLA,
  title={Ap\'ery limits and Mahler measures},
  author={Wadim Zudilin},
  year={2021}
}
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

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TLDR
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
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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
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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
A FEW REMARKS ON LINEAR FORMS INVOLVING CATALAN'S CONSTANT
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
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