Vorlesungen über Zahlentheorie

Vorlesungen über Zahlentheorie (German for Lectures on Number Theory) is the name of several different textbooks of number theory. The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863. Others were written by Leopold Kronecker, Edmund Landau, and Helmut Hasse. They all cover elementary number theory, Dirichlet's theorem, quadratic fields and forms, and sometimes more advanced topics.

Based on Dirichlet's number theory course at the University of Göttingen, the Vorlesungen were edited by Dedekind and published after Lejeune Dirichlet's death. Dedekind added several appendices to the Vorlesungen, in which he collected further results of Lejeune Dirichlet's and also developed his own original mathematical ideas.

The Vorlesungen cover topics in elementary number theory, algebraic number theory and analytic number theory, including modular arithmetic, quadratic congruences, quadratic reciprocity and binary quadratic forms.

The contents of Professor John Stillwell's 1999 translation of the Vorlesungen are as follows

This translation does not include Dedekind's Supplements X and XI in which he begins to develop the theory of ideals.

The German titles of supplements X and XI are:

Chapters 1 to 4 cover similar ground to Gauss' Disquisitiones Arithmeticae, and Dedekind added footnotes which specifically cross-reference the relevant sections of the Disquisitiones. These chapters can be thought of as a summary of existing knowledge, although Dirichlet simplifies Gauss' presentation, and introduces his own proofs in some places.

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