xvi How to use this text

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3

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7

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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.