. . . if one desires to make development in arithmetic one should still research the masters no longer the students. N. H. Abel Heeke used to be one in every of the masters, and actually, the learn of Heeke L sequence and Heeke operators has completely embedded his identify within the textile of quantity thought. it's a infrequent prevalence while a grasp writes a easy booklet, and Heeke's Lectures at the concept of Algebraic Numbers has turn into a vintage. to cite one other grasp, Andre Weil: "To enhance upon Heeke, in a therapy alongside classical traces of the speculation of algebraic numbers, will be a futile and most unlikely job. " we have now attempted to stay as shut as attainable to the unique textual content in pre serving Heeke's wealthy, casual kind of exposition. In a really few cases we have now substituted smooth terminology for Heeke's, e. g. , "torsion loose team" for "pure team. " One challenge for a scholar is the inability of workouts within the ebook. notwithstanding, given the big variety of texts on hand in algebraic quantity concept, this isn't a significant concern. particularly we suggest quantity Fields via D. A. Marcus (Springer-Verlag) as a very wealthy resource. we want to thank James M. Vaughn Jr. and the Vaughn origin Fund for his or her encouragement and beneficiant help of Jay R. Goldman with out which this translation may by no means have seemed. Minneapolis George U. Brauer July 1981 Jay R.
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