xvi How to use this text 1 3 5 7 2 4 6 8 9 10 Figure 1. Diagram of chapter dependencies characters by means of primitive roots seems less conceptually demanding than even an epsilon of representation theory. The theorem of Siegel from Section 7.3 is also needed in Section 9.3. The Borel-Carath´ eodory lemma of Section 7.4 is also used to prove the Hadamard factorization theorem of Section 8.6. The Hadamard factorization theorem is needed in Section 9.4 as well as in Chapter 10. As usual, starred material may be omitted without loss of continuity. There are exercises at the end of the chapters, for which solutions are not provided. In addition to the end-of-chapter exercises, there is a chapter with a selection of other exercises with solutions. As a caution, some exercises have been marked with a dagger, because they require more work than the remainder. But they are for the most part not more diﬃcult in the sense of it being harder to see what to do. A Summary of Elementary and Algebraic Number Theory with a con- densed exposition of those concepts on which the book draws is available on the web. The Summary presupposes familiarity with groups, rings and fields. All results from elementary and algebraic number theory that are actually needed in this book are proved in the Summary.

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