by J. S. Milne
Number of pages: 113
These are preliminary notes for a modern account of the theory of complex multiplication. The reader is expected to have a good knowledge of basic algebraic number theory, and basic algebraic geometry, including abelian varieties.
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by William Stein - University of Washington
Topics in this book: Rings of integers of number fields; Unique factorization of ideals in Dedekind domains; Structure of the group of units of the ring of integers; Finiteness of the group of equivalence classes of ideals of the ring of integers...
by Y. Kitaoka - Tata Institute of Fundamental Research
This book is concerned with the problem of representation of positive definite quadratic forms by other such forms. From the table of contents: Preface; Fourier Coefficients of Siegel Modular Forms; Arithmetic of Quadratic Forms.
by F. Oggier - Nanyang Technological University
Contents: Algebraic numbers and algebraic integers (Rings of integers, Norms and Traces); Ideals (Factorization and fractional ideals, The Chinese Theorem); Ramification theory; Ideal class group and units; p-adic numbers; Valuations; p-adic fields.
by Henri Darmon, Shou-Wu Zhang - Cambridge University Press
This volume has the Gross-Zagier formula and its avatars as a common unifying theme. It covers the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics.