Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics)

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Advanced Topics in the Arithmetic of Elliptic Curves Graduate Texts in Mathematics

The very numerous algorithms used are essentially all described in A Course in Com putational Algebraic Number Theory, GTM , first published in third corrected printing , which is referred to here as [CohO]. That text also treats other subjects such as elliptic curves, factoring, and primality testing. Itis important and natural to generalize these algorithms.

Henri Cohen. The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations.

The practical com pletion of this task sometimes known as the Dedekind program has been one of the major achievements of computational number theory in the past ten years, thanks to the efforts of many people. The very numerous algorithms used are essentially all described in A Course in Com putational Algebraic Number Theory, GTM , first published in third corrected printing , which is referred to here as [CohO]. That text also treats other subjects such as elliptic curves, factoring, and primality testing.

Cohen H. Advanced Topics in Computational Number Theory

Several gener alizations can be considered, but the most important are certainly the gen eralizations to global function fields finite extensions of the field of rational functions in one variable overa finite field and to relative extensions ofnum ber fields. As in [CohO], in the present book we will consider number fields only and not deal at all with function fields.


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Im Buch. Inhalt II.

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An Introduction to the Langlands Program D. Bibliografische Informationen.