與一類半乘法函數(shù)相關(guān)聯(lián)矩陣的行列式的界.pdf

1、四川大學碩士學位論文與一類半乘法函數(shù)相關(guān)聯(lián)矩陣的行列式的界姓名：楊勇申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：洪紹方20050410四川大學碩士學位論文BoundsfordeterminantsofmatricesassociatedwithclassesofsemimultiplicativefunctionsMajoring：MathematicsStudent：YongYangSupervisor：ProfessorShaofan

2、gHongLet，beallarithmeticalfunctionands=zl，，zn)beasetofndistinctpositiveintegersLet(，pi，j町1)denotethen禮matrixhaving，evaluatedattheleastcomlnonmultiplek，q】ofXiandqaSitsi，JentryInthispaperweshowthefollowingresults：TheoremlL

3、et，beasemi—multiplicativefunctionIf1∈l％：=，1[z∈sdlxl====(fp)(d)≥o)，JtheneachofthefollowingiStrue：fI【m。)1?！?了1p)(d)s＆=ld陸k。d枉to‘￡t(ii)Thennmatrix(f[xi，?；?ispositivesemidefiniteTheorem2Letebeapositiveintegerand，【。)denotefi

4、lecthDirichletconvo—lutionof，F(xiàn)orz∈z，wede6ne南：=0if，(c)(z)=0If，∈凸and，isamultiplicativefunction，theneachofthefollowingistrue：nnk=l(，(。)(鞏))24_I上)(d)S1如‘‘贏習)≤亟確11k=。(ii)Thennmatrix(贏)ispositivesemidefiniteKeywords：arithmetic