Bannar-Martin, Mark William2024-08-132024-08-1319981998https://hdl.handle.net/1828/17159For square-free m, the imaginary quadratic number fields Q/square root m of class number 1 occur when m = -1 , -2, -3, -7, -11, -19 -43, -67, -163. The unique factorization of algebraic integers in these number fields allows an elementary derivation of nine series involving ϖ and of nine algebraic identities. Full details of the calculation of these series and identities are given.45 pagesAvailable to the World Wide WebSome consequences of unique factorization in imaginary quadratic number fields of class number 1Thesis