## Analytic arithmetic of algebraic function fields |

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### Contents

Introduction l | 1 |

Additive Arithmetical Semigroups Satisfying Axiom A | 5 |

The Generating Function | 18 |

Copyright | |

12 other sections not shown

### Common terms and phrases

a e G absolutely convergent abstract prime number additive arithmetical semigroup algebraic function fields algebraic number fields analogue analytic function analytic number theory arithmetical functions arithmetical semigroup satisfying associated additive arithmetical asymptotic density asymptotic formula average value cardinal q categories F coefficients conclusion consequences of Axiom consider context coprime Corollary l0.2 D-algebra deduce denote the total discussed divisor function elementary elements of degree elements of G equation estimate Euler product Example l.3 finite fields finite modules follows function on G G of degree Hence implies indecomposable modules isomorphic Lemma Let f maximum order mean-value MObius function modules and algebras modules in F modules of cardinal non-isomorphic number fields number of elements order of magnitude PIM-function polynomial ring positive integer power series prime number theorem prime-independent proof of Theorem real-valued relative semigroup G semigroup satisfying Axiom subject to Axiom Theorem 3.l total number zeta function