In Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2. Their congruence provided a unified setting for many congruences proved previously by other authors using various means. The Hardy-Williams idea was as follows. Let d be the discriminant of a quadratic field. Suppose that d is odd and let d = PIP2. . . Pn be its unique decomposition into prime discriminants. Then, for any positive integer k coprime with d, the congruence holds trivially as each...
In Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fi...
This book provides a comprehensive and up-to-date treatment of research carried out in the last twenty years on congruences involving the values of L-functions (attached to quadratic characters) at certain special values. There is no other book on the market which deals with this subject. The book presents in a unified way congruences found by many authors over the years, from the classical ones of Gauss and Dirichlet to the recent ones of Gras, Vehara, and others. Audience: This book is aimed at graduate students and researchers interested in (analytic) number theory, functions of a complex...
This book provides a comprehensive and up-to-date treatment of research carried out in the last twenty years on congruences involving the values of L-...
