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This book contains the full text of the mathematical notebooks of Helmut Hasse (18981979), who was one of the leading mathematicians of the 20th century. The originals have been preserved in the Handschriftenabteilung at the Göttingen University Library. There are a total of seven volumes which contain 98 entries all together; these span the time period from July 1923 to February 1935. Each of the entries is preceded by a short comment. An extensive bibliography is provided. Compared to the other documents and papers from Hasse Nachlass at Göttingen, these papers are quite different. They detail Hasse‘s mathematical background, interests and his way of approaching problems. Many of the entries are inspired by Hasse‘s discussions with other mathematicians (for example, Emil Artin is often mentioned). One of the notable highlights in the entries is the first documentation of Artin‘s conjecture on primitive roots (1927), which Hasse noted down after a discussion with Artin. Another example is the first proof of the Riemann hypothesis for an extended class of function fi elds of high genus, namely those of the generalised Fermat fields with a finite field of constants (1932), after corresponding with Harold Davenport.
Notebooks  Göttingen University Library  Harold Davenport  Emil Artin  Riemann Hypothesis
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This book reproduces the complete extant correspondence between Emmy Noether and Helmut Hasse. There are 82 such letters, of which 79 are from Noether to Hasse, dating from 1925 until Noether's sudden death in 1935. The correspondence reflects a crucial period in the development of 20th century algebra and number theory, in particular class field theory. Details of proofs appear alongside with conjectures and speculations. Also discussed are questions of textbook presentation, e.g., of Galois theory. Aside from mathematical details, the spontaneity of Noether's style allows many glimpses at the image that Emmy Noether and Helmut Hasse had of the topics they were working in. The Hasse  Noether correspondence is a rich source for those who are interested in the rise and the development of mathematical notions and ideas. Each letter is accompanied by a detailed commentary supplied by the editors. For the convenience of the reader, numerous crossreferences, extended indexes, and short biographies of all persons mentioned in the correspondence have been added.
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This book contains the full text of the letters from Emil Artin to Helmut Hasse, as they are preserved in the Handschriftenabteilung of the Göttingen University Library. There are 49 such letters, written in the years 19231934, discussing mathematical problems of the time. The corresponding letters in the other direction, i.e., from Hasse to Artin, seem to be lost. We have supplemented Artin‘s letters by detailed comments, combined with a description of the mathematical environment of Hasse and Artin, and of the relevant literature. In this way it has become possible to sufficiently reconstruct the content of the corresponding letters from Hasse to Artin too. Artin and Hasse were among those who shaped modern algebraic number theory, in particular class field theory. Their correspondence admits a view of the ideas which led to the great achievements of their time, starting from Artin‘s Lseries and his reciprocity law towards Hasse‘s norm symbol, local class field theory and the LocalGlobal Principle. These letters are a valuable source for understanding the rise and development of mathematical ideas and notions as we see them today. The book is a followup of our earlier book on the correspondence between Hasse and Emmy Noether. It is thus the second of a series which aims to open access to the rich collection of Hasse‘s mathematical letters and notes contained in the Göttingen Handschriftenabteilung.
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