Contents XV A2.2 Representations 612 A2.2.1 Equivalence and reducibility 612 A2.2.2 Orthogonality 613 A2.2.3 The regular representation 614 A2.3 Fourier transforms 615 Appendix 3:The Solovay-Kitaev theorem 617 Appendix 4:Number theory 625 A4.1 Fundamentals 625 A4.2 Modular arithmetic and Euclid's algorithm 626 A4.3 Reduction of factoring to order-finding 633 A4.4 Continued fractions 635 Appendix 5:Public key cryptography and the RSA cryptosystem 640 Appendix 6:Proof of Lieb's theorem 645 Bibliography 649 Index 665Contents xv A2.2 Representations 612 A2.2.1 Equivalence and reducibility 612 A2.2.2 Orthogonality 613 A2.2.3 The regular representation 614 A2.3 Fourier transforms 615 Appendix 3: The Solovay--Kitaev theorem 617 Appendix 4: Number theory 625 A4.1 Fundamentals 625 A4.2 Modular arithmetic and Euclid’s algorithm 626 A4.3 Reduction of factoring to order-finding 633 A4.4 Continued fractions 635 Appendix 5: Public key cryptography and the RSA cryptosystem 640 Appendix 6: Proof of Lieb’s theorem 645 Bibliography 649 Index 665