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. . . if one wants to make progress in mathematics one should study
the masters not the pupils. N. H. Abel Heeke was certainly one of
the masters, and in fact, the study of Heeke L series and Heeke
operators has permanently embedded his name in the fabric of number
theory. It is a rare occurrence when a master writes a basic book,
and Heeke's Lectures on the Theory of Algebraic Numbers has become
a classic. To quote another master, Andre Weil: "To improve upon
Heeke, in a treatment along classical lines of the theory of
algebraic numbers, would be a futile and impossible task. " We have
tried to remain as close as possible to the original text in pre
serving Heeke's rich, informal style of exposition. In a very few
instances we have substituted modern terminology for Heeke's, e.
g., "torsion free group" for "pure group. " One problem for a
student is the lack of exercises in the book. However, given the
large number of texts available in algebraic number theory, this is
not a serious drawback. In particular we recommend Number Fields by
D. A. Marcus (Springer-Verlag) as a particularly rich source. We
would like to thank James M. Vaughn Jr. and the Vaughn Foundation
Fund for their encouragement and generous support of Jay R. Goldman
without which this translation would never have appeared.
Minneapolis George U. Brauer July 1981 Jay R."
. . . if one wants to make progress in mathematics one should study
the masters not the pupils. N. H. Abel Heeke was certainly one of
the masters, and in fact, the study of Heeke L series and Heeke
operators has permanently embedded his name in the fabric of number
theory. It is a rare occurrence when a master writes a basic book,
and Heeke's Lectures on the Theory of Algebraic Numbers has become
a classic. To quote another master, Andre Weil: "To improve upon
Heeke, in a treatment along classical lines of the theory of
algebraic numbers, would be a futile and impossible task. " We have
tried to remain as close as possible to the original text in pre
serving Heeke's rich, informal style of exposition. In a very few
instances we have substituted modern terminology for Heeke's, e.
g., "torsion free group" for "pure group. " One problem for a
student is the lack of exercises in the book. However, given the
large number of texts available in algebraic number theory, this is
not a serious drawback. In particular we recommend Number Fields by
D. A. Marcus (Springer-Verlag) as a particularly rich source. We
would like to thank James M. Vaughn Jr. and the Vaughn Foundation
Fund for their encouragement and generous support of Jay R. Goldman
without which this translation would never have appeared.
Minneapolis George U. Brauer July 1981 Jay R."
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