Yuliya Krylova

Kharaktery Dirikhle I Tsiklicheskie Rasshireniya Polya Ratsional'nykh Chisel: Monografiya Yuliya Krylova Russian edition

V pervoy glave podrobno izuchaetsya teoriya tsepnykh drobey. Byli izucheny predstavleniya ratsional'nykh i irratsional'nykh chisel v vide tsepnykh drobey. Dalee izucheny podkhodyashchie drobi dlya tsepnykh drobey. Tak zhe byli dokazany naglyadnye formuly dlya vychisleniya chisliteley i znamenateley podkhodyashchikh drobey, i privedeny otsenki dlya posledovatel'nostey podkhodyashchikh drobey. V sleduyushchem paragrafe rassmatrivalsya klass diofantovykh uravneniy vtoroy stepeni, nazyvaemye uravneniyami Pellya. Privoditsya teorema o sushchestvovanii netrivial'nogo resheniya uravneniy Pellya. Byli dokazany neskol'ko utverzhdeniy, i postroen algoritm dlya otyskaniya resheniy uravneniy Pellya s pomoshch'yu metoda tsepnykh drobey. Rassmatrivaetsya prilozhenie uravneniy Pellya dlya otyskaniya edinits v kvadratichnykh rasshireniyakh polya veshchestvennykh chisel. Byli naydeny edinitsy v sluchae deystvitel'nogo i mnimogo rasshireniya. Vo vtoroy glave prodolzhaetsya izuchenie kvadratichnykh rasshireniy. Byli naydeny kvadratichnye i nekotorye kubicheskie kharaktery, postroeny tablitsy kharakterov i vyveden vid naimen'shego perioda kak kvadratichnogo, tak i kubicheskogo kharakterov.