Solutions to Introduction to Analytic Number Theory by Tom M. Apostol

Preface......Page 2 1 The Fundamental Theorem of Arithmetic......Page 4 2 Arithmetical Functions and Dirichlet Multiplication......Page 14 3 Averages of Arithmetical Functions......Page 35 4 Some Elementary Theorems on the Distribution of Prime Numbers......Page 54 5 Congruences......Page 76 6 Finite Abelian Groups and Their Characters......Page 87 7 Dirichlet's Theorem on Primes in Arithmetic Progressions......Page 95 8 Periodic Arithmetic Functions and Gauss Sums......Page 99 9 Quadratic Residues and the Quadratic Reciprocity Law......Page 110 10 Primitive Roots......Page 119 11 Dirichlet Series and Euler Products......Page 129 12 The Functions (s) and L(s, )......Page 144 13 Analytic Proof of the Prime Number Theorem......Page 163 14 Partitions......Page 173 End......Page 188