Multiplicative Number Theory

Front Matter....Pages i-xiii
Primes in Arithmetic Progression....Pages 1-11
Gauss’ Sum....Pages 12-16
Cyclotomy....Pages 17-26
Primes in Arithmetic Progression: The General Modulus....Pages 27-34
Primitive Characters....Pages 35-42
Dirichlet’s Class Number Formula....Pages 43-53
The Distribution of the Primes....Pages 54-58
Riemann’s Memoir....Pages 59-64
The Functional Equation of the L Functions....Pages 65-72
Properties of the Γ Function....Pages 73-73
Integral Functions of Order 1....Pages 74-78
The Infinite Products for ξ( s ) and ξ( s, χ )....Pages 79-83
A Zero-Free Region for ζ(s)....Pages 84-87
Zero-Free Regions for L ( s, χ )....Pages 88-96
The Number N ( T )....Pages 97-100
The Number N ( T, χ )....Pages 101-103
The Explicit Formula for Ψ( x )....Pages 104-110
The Prime Number Theorem....Pages 111-114
The Explicit Formula for ψ( x , χ)....Pages 115-120
The Prime Number Theorem for Arithmetic Progressions (I)....Pages 121-125
Siegel’s Theorem....Pages 126-131
The Prime Number Theorem for Arithmetic Progressions (II)....Pages 132-134
The Pólya-Vinogradov Inequality....Pages 135-137
Further Prime Number Sums....Pages 138-142
An Exponential Sum Formed with Primes....Pages 143-144
Sums of Three Primes....Pages 145-150
The Large Sieve....Pages 151-160
Bombieri’s Theorem....Pages 161-168
An Average Result....Pages 169-171
References to other Work....Pages 172-174
Back Matter....Pages 175-177