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PDF-2PeterSarnakandJacobTsimerman(heree(z)=e2iz).ItfollowsfromWeil'sbound PDF document

c2wherecisthenumberofdivisorsofcLinniksConjectureassertsthatfor0andxp jnjXcxS1nc cx3Notethatfrom2wehavethatXcxjSmncj cp xxmn4Ontheotherhandformn xedMichelMis

c(2)where(c)isthenumberofdivisorsofc.Linnik'sConjectureassertsthatfor0andxp jnjXcxS(1;n;c) cx:(3)Notethatfrom(2)wehavethatXcxjS(m;n;c)j cp x(x(m;n)):(4)Ontheotherhandform;n xed Michel[Mi]s

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