Corpus ID: 237563215

Mahler measure numerology

  title={Mahler measure numerology},
  author={Wadim Zudilin},
|x1|=···=|xk|=1 log |P (x1, . . . , xk)| dx1 x1 · · · dxk xk of an k-variable (Laurent) polynomial P (x1, . . . , xk) ∈ C[x1, . . . , xk] is a quite unique attractor of numerous problems in mathematics [3]. One of big problems (well open even in the case k = 1!) is the range of the Mahler measures attached to polynomials with integer coefficients [1]. A particular aspect of this problem is a remarkable connection of such Mahler measures to the L-values of algebraic varieties, usually related to… Expand


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
Many Variations of Mahler Measures
The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, specialExpand
Deligne periods of mixed motives, -theory and the entropy of certain ℤⁿ-actions
For a coherent sheaf M on the split n-torus Gn A = spec A[7n] over a commutative ring A there is a natural En-action on its group of global sections F(M) = F(G AA, M). If we give F(M) the discreteExpand
Number Theory and Related Fields, In Memory of Alf van der Poorten
Preface.- Life and Mathematics of Alfred Jacobus van der Poorten (D. Hunt).- Ramanujan-Sato-Like Series (G. Almkvist, J. Guillera).- On the Sign of the Real Part of the Riemann Zeta Function (J.Expand
On identity
The first result is: identity (1), which is valid for each pair of complex numbers a, x such that a ^ 0 and \x < 1. Expand
Modular Mahler Measures I
We relate Boyd’s numerical examples, linking the Mahler measure m(P k ) of certain polynomials P k to special values of L-series of elliptic curves, to the Bloch-Beilinson conjectures. We study m(P kExpand
Period(d)ness of L-Values
  • W. Zudilin
  • Geography, Computer Science
  • Number Theory and Related Fields
  • 2013
The novelty of the new analytical machinery introduced to write the values L(E, 2) of L-series of elliptic curves as periods in the sense of Kontsevich and Zagier is outlined and two illustrative period evaluations are provided for a conductor 32 elliptic curve E. Expand
The L-Functions and Modular Forms Database Project
  • J. Cremona
  • Mathematics, Computer Science
  • Found. Comput. Math.
  • 2016
In the lecture, I gave a very brief introduction to L-functions for non-experts and explained and demonstrated how the large collection of data in the LMFDB is organized and displayed, showing the interrelations between linked objects, through the website Expand
Short Walk Adventures
We review recent development of short uniform random walks, with a focus on its connection to (zeta) Mahler measures and modular parametrisation of the density functions. Furthermore, we extendExpand
Speculations concerning the range of Mahler's measure