Multiplicative Number Theory

Description

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