Several problems from number theory ; Kai kurie skaičių teorijos uždaviniai

VILNIUS UNIVERSITYGiedrius AlkauskasSeveral problems from number theoryDoctoral dissertationPhysical sciences, mathematics (01 P)Vilnius, 20091The work on this dissertation was performed in 2006-2009 at Vilnius University.Scientific supervisor:Prof. Dr. Habil. Antanas Laurinˇcikas (Vilniaus University, Physical sciences, Mathematics- 01 P).2VILNIAUS UNIVERSITETASGiedrius AlkauskasKai kurie skaiˇciu¸ teorijos uˇzdaviniaiDaktaro disertacijaFiziniai mokslai, matematika (01 P)Vilnius, 20093Disertacija rengta 2006-2009 metais Vilniaus Universitete.Mokslinis vadovas:Prof. habil. dr. Antanas Laurinˇcikas (Vilniaus universitetas, fizinai mokslai, matematika -01 P).4ContentsContents 50.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70.1.1 Actuality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70.1.2 Aims and problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70.1.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.1.4 Novelty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.1.5 Statements presented for the defence . . . . . . . . . . . . . . . . . . 80.1.6 History of the problem and main results . . . . . . . . . . . . . . . . 80.1.7 Approbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110.1.8 Principal publications . . . . . . . . . . . . . . . . . . . . . . . . . .