Errata of “Isoparametric hypersurfaces with $(g,m)=(6,2)$”
We give a correction of the proof of the homogeneity of isoparametric hypersurfaces with $(g,m)=(6,2)$.
View ArticleMultiplicative functions in short intervals
We introduce a general result relating “short averages” of a multiplicative function to “long averages” which are well understood. This result has several consequences. First, for the Möbius function...
View ArticleClassicité de formes modulaires surconvergentes
Nous généralisons le critère de classicité de formes modulaires surconvergentes sur les courbes modulaires dû à Coleman à certaines variétés de Shimura PEL de type (A) et~(C) associées à des groupes...
View ArticleLarge gaps between consecutive prime numbers
Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdős, we show that \[ G(X) \geq f(X) \frac{\log X \log \log X \log \log \log \log X}{(\log...
View ArticleLarge gaps between primes
We show that there exist pairs of consecutive primes less than $x$ whose difference is larger than \[ t(1+o(1))(\log{x})(\log\log{x})(\log\log\log\log{x})(\log\log\log{x})^{-2}\] for any fixed $t$....
View ArticleDecay for solutions of the wave equation on Kerr exterior spacetimes III: The...
This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I–II: the cases $|a| \ll M$ or axisymmetry,...
View ArticleHomological stability for Hurwitz spaces and the Cohen-Lenstra conjecture...
We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let $\ell > 2$ be...
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