Mesure de Mahler d'hypersurfaces K3

Mesures de Mahler et équidistribution logarithmique

Let X be a projective integral normal scheme over a number field F; let L be a ample line bundle on X together with a semi-positive adelic metric in the sense of Zhang. The main results of this article are 1) A formula which computes the height (relative to L) of a Cartier divisor D on X as generalized "Mahler measures", i.e. by integrating Green functions for D against measures attached to L. 2) a theorem of equidistribution of points of "small" height valid for functions with logarithmic singularities along a divisor D, provided the height of D is "minimal". In the context of algebraic dynam…

A Mahler measure of a K3-hypersurface expressed as a Dirichlet L-series

We present another example of a 3-variable polynomial defining a K3-hypersurface and having a logarithmic Mahler measure expressed in terms of a Dirichlet L-series.

环面簇中超曲面的算术体积与Mahler测度

The arithmetic volume of hypersurfaces in toric varieties and Mahler measures

该研究确定了光滑射影环面簇中超曲面的典范算术体积，并由此证明了这类超曲面上的广义Hodge指标定理，为算术代数几何领域相关问题提供了新结果。

Mahler Measure of 3D Landau-Ginzburg Potentials

We express the Mahler measures of $23$ families of Laurent polynomials in terms of Eisenstein-Kronecker series. These Laurent polynomials arise as Landau-Ginzburg potentials on Fano $3$-folds, $16$ of which define $K3$ hypersurfaces of generic Picard rank $19$, and the rest are of generic Picard rank $< 19$. We relate the Mahler measure at each rational singular moduli to the value at $3$ of the $L$-function of some weight-$3$ newform. Moreover, we find $10$ exotic relations among the Mahler measures of these families.