Mahler measure for dynamical systems on ℙ1 and intersection theory on a singular arithmetic surface
Mahler measure for dynamical systems on ℙ1 and intersection theory on a singular arithmetic surface
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ℙ1 动力系统的马勒测度和奇异算术曲面上的相交理论
DOI：
10.1007/0-8176-4417-2_10
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
T. Tucker
中科院分区：
文献类型：
--
作者：
J. Pineiro;L. Szpiro;T. Tucker
马勒测度公式将代数数的高度表示为单位圆上其最小多项式的绝对值的对数的积分。高度实际上是与单项映射xn相关联的规范高度。我们证明了，对于任意有理映射f（x），一个代数数关于f（x）的标准高度可以表示为它的方程的对数对与f（x）相关的不变Brolin-Lyubich测度的积分，在有限个差约化的地方有额外的adelic项。我们给出了一个完整的证明，这个定理使用积分模型的每个。在关于等分布和Julia集的最后一章中，我们对P. Autissier，M.贝克河，巴西-地鲁米利和我们自己。特别是我们的结果，结合技术的丢番图近似，将使我们能够计算积分的广义马勒公式平均周期点。
The Mahler measure formula expresses the height of an algebraic number as the integral of the log of the absolute value of its minimal polynomial on the unit circle. The height is in fact the canonical height associated to the monomial mapsxn. We show in this work that for any rational mapϕ(x)the canonical height of an algebraic number with respect toϕcan be expressed as the integral of the log of its equation against the invariant Brolin-Lyubich measure associated toϕ, with additional adelic terms at finite places of bad reduction. We give a complete proof of this theorem using integral models for each iterate ofϕ. In the last chapter on equidistribution and Julia sets we give a survey of results obtained by P. Autissier, M. Baker, R. Rumely and ourselves. In particular our results, when combined with techniques of diophantine approximation, will allow us to compute the integrals in the generalized Mahler formula by averaging on periodic points.
DOI：
10.1090/s0894-0347-1994-1260106-x
发表时间：
1994-01
影响因子：
3.9
作者：
J. Bost;H. Gillet;C. Soulé
通讯作者：
J. Bost;H. Gillet;C. Soulé