Ebook: Multiplicative Number Theory

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Content:
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 ? Function....Pages 73-73
Integral Functions of Order 1....Pages 74-78
The Infinite Products for ?(s) and ?(s, ?)....Pages 79-83
A Zero-Free Region for ?(s)....Pages 84-87
Zero-Free Regions for L(s, ?)....Pages 88-96
The Number N(T)....Pages 97-100
The Number N(T, ?)....Pages 101-103
The Explicit Formula for ?(x)....Pages 104-110
The Prime Number Theorem....Pages 111-114
The Explicit Formula for ?(x, ?)....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 P?lya-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

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Content:
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 ? Function....Pages 73-73
Integral Functions of Order 1....Pages 74-78
The Infinite Products for ?(s) and ?(s, ?)....Pages 79-83
A Zero-Free Region for ?(s)....Pages 84-87
Zero-Free Regions for L(s, ?)....Pages 88-96
The Number N(T)....Pages 97-100
The Number N(T, ?)....Pages 101-103
The Explicit Formula for ?(x)....Pages 104-110
The Prime Number Theorem....Pages 111-114
The Explicit Formula for ?(x, ?)....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 P?lya-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
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