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Index
                        78
                          nonvanishing of, see
                                                               second proof of, 70–72
                            Nonvanishing of L-series           first proof of, 68–70
                          zero of any, 63                    Pringsheim-Landau Theorem, 59
                        Lagrange theorem, 49                 Progressions, arithmetic, see
                        Landau corollary, 69                     Arithmetic progressions
                        L’Hˆ opital’s rule, 5
                                                             q(n), coefficients of, 25–29
                        “Magnitude property,” 53
                        Mathematics, vii                     Relative error, 4
                        “Monotone majorant,” 45              Representation functions, 7
                                                               generating functions of, 7
                        “Natural” proof, 59                    near constancy of, 31
                          of nonvanishing of L-series,       Riemann integral, 20
                            59–63                              double, 31
                        Nonnegative integers, splitting,     Riemann sums, 20–25
                            8–10                             Roth Theorem, 46–47
                        Nonvanishing of L-series, 60         Rulers, marks on, 12–13
                          “natural” proof of, 59–63
                                                             Schnirelmann’s Theorem, 50–51
                        Odds and evens, dissection into,     Schwarz inequality, 34
                            14                               Sequences without arithmetic
                                                               progressions, 41–47
                        Parseval upper bound, 36             Splitting problem, 8–10
                        Parseval’s identity, 33–34           Stirling’s formula, 4, 27, 29
                        Partial fractional decomposition,    Szemer´ edi-Furstenberg result, 43
                            3–4
                        Partition function, 17–29            Taylor coefficients, 3
                        Permission constant, 42              Tchebychev’s observation, 70
                        Pigeonhole principle, 50
                        PNT, see Prime Number Theorem        Unit circle, 13
                        Prime Number Theorem (PNT),
                            65                               Waring problem, 49–56
                          analytic proof of, 65–71           Weyl sums, 51–52
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