作者：Matomaki, Kaisa; Radziwill, Maksym; Shao, Xuancheng; Tao, Terence; Teravainen, Joni
作者单位：University of Turku; Northwestern University; University of Kentucky; University of California System; University of California Los Angeles; University of Cambridge
摘要：We study higher uniformity properties of the von Mangoldt function Lambda, the M & ouml;bius function mu, and the divisor functions d(k) on short intervals(x, x+H]for almost all x is an element of[X,2X].Let Lambda(& sharp;)and d(k)(& sharp;)be suitable approximants of Lambda and d(k) ,G/ Gamma a filtered nilmanifold, and F:G/ Gamma ->& Copf;a Lipschitz function. Then our results imply for instance that when X1/3+epsilon <= H <= Xwe have, for almost all x is an element of[X,2X], sup(g is an ele...
作者：Toma, Radu
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：Let N be a prime and phi be a Hecke-Maa ss cuspidal newform for the Hecke congruence subgroup Gamma 0(N) in SLn(R). We define a notion of the bulk Omega N of the space Gamma 0(N)\SLn(R)/SO(n) with respect to a compact set Omega subset of SLn(R). For any prime n, we prove sub-baseline bounds for the sup-norm of phi restricted to Omega N. Conditionally on GRH, we generalise this result to all n >= 2. The methods involve a new reduction theory with level structure, based on generalisations of Atk...
