Collected works. Ed. by L. Mirsky, I. J. Schoenberg, W. Schwarz, H. Wefelscheid. Volume 1.

*(English)*Zbl 0653.01018
Essen (FRG): Thales Verlag. 415 p. DM 224.00 (1984).

Edmund Landau left, at his death in 1938, a complete collection of his 255 papers (excluding his books), arranged chronologically, and with marginal annotations in Landau’s hand. This collection has been used as the basis for a ten-volume edition of Landau’s works of which volume ten is planned to contain various biographical materials including photographs and facsimiles.

In addition, various commentaries on Landau’s papers or his work are included. While it may seem unusual for the collected works of a mathematician who died over fifty years ago to be now appearing, this publication is much more than simply an honoring of Landau’s memory, something impossible at his death in a Germany ruled by the Nazis who had forced him in 1933 to relinquish his professorial chair at GĂ¶ttingen. Indeed Landau’s work was so stimulating, and so deeply imbued with the pedagogical impulse, that stimulus can still be found in reading it. This publication also serves to make clear how Landau’s results fit into the picture of contemporary mathematics.

Because Landau’s papers will be reprinted in the chronological order of their appearance, most remarks about this and subsequent volumes will be addressed to the critical apparatus and other materials contained in them.

This first volume of the ten contains no commentary on the papers and the ones reprinted in it are preceded by the well-known obituary of Landau by G. H. Hardy and H. Heilbronn [J. Lond. Math. Soc. 13, 302–310 (1938; Zbl 0019.38905)] and a somewhat less-known address by L. Mirsky, “In memory of Edmund Landau” given to celebrate the centennial of his birth [Math. Sci. 2, 1–26 (1977; Zbl 0358.01016)]. Both of these are still very much worth reading, Mirsky’s essay both being more personal, and containing more biographical material. The papers, from Landau’s first publication, when he was 18, in Deutsches Wochenschach (a suggestion, using systems of linear equations, for fair allocation of prizes, in chess tournaments) through to number 21 in 1903 which was concerned with the maximal order of a permutation of \(n\) elements.

Number 3 is Landau’s well-known doctoral dissertation in 1899, when he was 22, on a new proof that \(\sum^{\infty}_{n=1}\frac{\mu (n)}{n}=0\) (at Berlin). It is interesting to note that, in the style of the time, two of the three “opponents” of Landau’s dissertation and the five “theses” which he also undertook to defend were Fritz Hartogs and Ernst Steinitz.

Number 16 (1903) contains Landau’s then new method of proving the prime number theorem, and the proof of the prime ideal theorem along similar lines.

At the end of the volume is a complete list of Landau’s publications (which is to be repeated at the end of Vols. 2 and 10).

As frontispiece is a picture of Landau at his desk.

The mathematical public owes a debt of gratitude to the editors for finally making Landau’s Collected Works available, and the reader of this and subsequent volumes will discover that there are different “Landau- styles”, but always theorems presented efficiently and carefully.

In addition, various commentaries on Landau’s papers or his work are included. While it may seem unusual for the collected works of a mathematician who died over fifty years ago to be now appearing, this publication is much more than simply an honoring of Landau’s memory, something impossible at his death in a Germany ruled by the Nazis who had forced him in 1933 to relinquish his professorial chair at GĂ¶ttingen. Indeed Landau’s work was so stimulating, and so deeply imbued with the pedagogical impulse, that stimulus can still be found in reading it. This publication also serves to make clear how Landau’s results fit into the picture of contemporary mathematics.

Because Landau’s papers will be reprinted in the chronological order of their appearance, most remarks about this and subsequent volumes will be addressed to the critical apparatus and other materials contained in them.

This first volume of the ten contains no commentary on the papers and the ones reprinted in it are preceded by the well-known obituary of Landau by G. H. Hardy and H. Heilbronn [J. Lond. Math. Soc. 13, 302–310 (1938; Zbl 0019.38905)] and a somewhat less-known address by L. Mirsky, “In memory of Edmund Landau” given to celebrate the centennial of his birth [Math. Sci. 2, 1–26 (1977; Zbl 0358.01016)]. Both of these are still very much worth reading, Mirsky’s essay both being more personal, and containing more biographical material. The papers, from Landau’s first publication, when he was 18, in Deutsches Wochenschach (a suggestion, using systems of linear equations, for fair allocation of prizes, in chess tournaments) through to number 21 in 1903 which was concerned with the maximal order of a permutation of \(n\) elements.

Number 3 is Landau’s well-known doctoral dissertation in 1899, when he was 22, on a new proof that \(\sum^{\infty}_{n=1}\frac{\mu (n)}{n}=0\) (at Berlin). It is interesting to note that, in the style of the time, two of the three “opponents” of Landau’s dissertation and the five “theses” which he also undertook to defend were Fritz Hartogs and Ernst Steinitz.

Number 16 (1903) contains Landau’s then new method of proving the prime number theorem, and the proof of the prime ideal theorem along similar lines.

At the end of the volume is a complete list of Landau’s publications (which is to be repeated at the end of Vols. 2 and 10).

As frontispiece is a picture of Landau at his desk.

The mathematical public owes a debt of gratitude to the editors for finally making Landau’s Collected Works available, and the reader of this and subsequent volumes will discover that there are different “Landau- styles”, but always theorems presented efficiently and carefully.

Reviewer: Sanford L. Segal (Rochester)

##### MSC:

01A75 | Collected or selected works; reprintings or translations of classics |

01A70 | Biographies, obituaries, personalia, bibliographies |