Class Numbers: Quadratic and Cyclotomic Fields.

      Аннотация: The class number problem of quadratic fields is one of the oldest problems in number theory. Now a days researchers expanding this problem in different directions not only for quadratic fields but also for other number fields. This monograph offers a clear, efficient and recent expositions of some aspects of class number problem of quadratic fields as well as cyclotomic fields. Topics include: fundamental concepts of number fields with special reference to quadratic and cyclotomic fields; class numbers of real, imaginary quadratic fields and cyclotomic; discriminant of quadratic fields. Some new topic: generalized Mersenne primes and their application in class number of quadratic fields; conjugate quadratic fields and their class numbers; equivalent quadratic fields and their class numbers. The monograph is suitable for graduate students and researchers.

Ключевые слова: Class Number Problems, Quadratic fields, Cyclotomic fields, Generalized Mersenne Primes