分类：教育/科学-理工学科-数学
问题：极限lim(n
lim(n->+∞)1/nΣ(k:1->n)e^2πimlgk,m∈Z\{0}.
Help！！！
回答：Unfortunately,thesequence{lg(k)}isnotuniformlydistributedmod1.Then,wecannotsafelyconcludethatthelimitis0duetoWeyl'scriterionwhichImentionedyoubefore. {kx}wherexisirrational,theanswerisdefinitely0.Atthisstage,letustryina :Asnapproachestoinfinite,e^(2πim*lgn)doesnothavealimit,thuswecanpredictthelimitdoesnotexist.However,themoduleofthefunctionexists.Since|e^(2πim*lgn)|=1.