Number Theory in the Spirit of Liouville (London Mathematical Society Student Texts)

JosephLiouvilleisrecognisedasoneofthegreatmathematiciansofthenineteenthcentury,andoneofhisgreatestachievementswastheintroductionofapowerfulnewmethodintoelementarynumbertheory.Thisbookprovidesagentleintroductiontothismethod,explainingitinaclearandstraightforwardmanner.Themanyapplicationsprovidedincludeapplicationstosumsofsquares,sumsoftriangularnumbers,recurrencerelationsfordivisorfunctions,convolutionsumsinvolvingthedivisorfunctions,andmanyothers.AllofthetopicsdiscussedhavearichhistorydatingbacktoEuler,Jacobi,Dirichlet,Ramanujanandothers,andtheycontinuetobethesubjectofcurrentmathematicalresearch.Williamsplacestheresultsintheirhistoricalandcontemporarycontexts,makingtheconnectionbetweenLiouville'sideasandmoderntheory.ThisistheonlybookinEnglishentirelydevotedtothesubjectandisthusanextremelyvaluableresourceforbothstudentsandresearchersalike.