作者：Mathieu Lewin , Elliott H. Lieb , Robert Seiringer 来源：[J].CEDRAM 摘要：In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density....
 作者：Stéphane Druel , Henri Guenancia 来源：[J].CEDRAM 摘要：In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, étale in codimension one, that decomposes as a product of an abelian variety, and singular a...
 作者：Yiwen Ding 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (4), pp.1457-1519CEDRAM 摘要：Let $F_{\wp }$ be a finite extension of $\mathbb{Q}_p$. By considering partially de Rham families, we establish a Colmez–Greenberg–Stevens formula (on Fontaine–Mazur $\mathcal{L}$-invariants) for (general) $2$-dimensional semi-stable non-crystalline representations of t...
 作者：Alessandro D’Andrea , Claudia Pinzari , Stefano Rossi 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (5), pp.2003-2027CEDRAM 摘要：Banica and Vergnioux have shown that the dual discrete quantum group of a compact simply connected Lie group has polynomial growth of order the real manifold dimension. We extend this result to a general compact group and its topological dimension, by connecting it with the ...
 作者：Yann Bugeaud , Dong Han Kim 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (5), pp.2225-2235CEDRAM 摘要：Let $r$ and $s$ be multiplicatively independent positive integers. We establish that the $r$-ary expansion and the $s$-ary expansion of an irrational real number, viewed as infinite words on $\lbrace 0, 1, \ldots , r-1\rbrace$ and $\lbrace 0, 1, \ldots , s-1\rbrace$, respective...
 作者：Stéphane Seuret , Adrián Ubis 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (5), pp.2237-2264CEDRAM 摘要：We are interested in the convergence and the local regularity of the lacunary Fourier series $F_s(x) = \sum _{n=1}^{+\infty } \frac{e^{2i\pi n^2 x}}{n^s}$. In the 1850’s, Riemann introduced the series $F_2$ as a possible example of nowhere differentiable function, and the st...
 作者：Teodor Banica 来源：[J].Annales mathématiques Blaise Pascal, 2017, Vol.24 (2), pp.195-224CEDRAM 摘要：We discuss an extension of the Weingarten formula, to the case of noncommutative homogeneous spaces, under suitable “easiness” assumptions. The spaces that we consider are noncommutative algebraic manifolds, generalizing the spaces of type $X=G/H\subset \mathbb{C}^N$, with $...  作者：Omar Anza Hafsa , Nicolas Clozeau , Jean-Philippe Mandallena 来源：[J].Annales mathématiques Blaise Pascal, 2017, Vol.24 (2), pp.135-193CEDRAM 摘要：We study periodic homogenization by$\Gamma $-convergence of integral functionals with integrands$W(x,\xi )$having no polynomial growth and which are both not necessarily continuous with respect to the space variable and not necessarily convex with respect to the matrix va...  作者：Veronique Fischer , Michael Ruzhansky 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (4), pp.1671-1723CEDRAM 摘要：In this article, we study the$L^p\$-properties of powers of positive Rockland operators and define Sobolev spaces on general graded Lie groups. We establish that the defined Sobolev spaces are independent of the choice of a positive Rockland operator, and that they are inter...
 作者：Meng Chen , Zhi Jiang 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (5), pp.2043-2082CEDRAM 摘要：We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove some optimal results in dimensions 4 and ...