## Lectures on advanced analytic number theory |

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### Contents

y Hwnmmnm ndmwﬁm H M | 28 |

APPLICATIONS OF KRONECKERS LIMIT FORMULAS | 73 |

2 Class number of the absolute class field of PJddf O | 99 |

8 other sections not shown

### Common terms and phrases

_ _ I I _ _ Q _ _I _ 1 _ _ I _ _ I I _ _ I_ _ O _ _ Q _ _ U _ _ v _ _I _ abelian algebraic number field analytic continuation class group class number converges absolutely cusp Dedekind defined denote entire function finite functional equation fundamental domain genus character half-plane Hence Hilbert modular I I _ _ I I I I_ _ ideal class ideal class group integral ideal Kronecker m+nz matrix modf modular forms modular function modular group modular transformation modulo f Moreover n-rowed narrow class obtain prime ideals Proposition prove Q _ _ quadratic form rational integers rational numbers ray class character ray classes modulo Riemann right hand side roots of unity summation tends to infinity theorem