- Title
- A Mahler Miscellany
- Creator
- Bugeaud, Yann; Coons Jr, Michael
- Relation
- Documenta Mathematica. Journal of the German Association of Mathematicians Vol. Extra Vol., p. 179-190
- Publisher Link
- http://dx.doi.org/10.25537/dm.2019.SB-179-190
- Publisher
- Deutsche Mathematiker-Vereinigung
- Resource Type
- journal article
- Date
- 2019
- Description
- Kurt Mahler’s first paper [M1] was published in 1927. Like most first papers from students, it came about for many reasons—certainly interest was one of them—but the setting was an important one. It was the mid-late 1920s in Germany, which was the place (and time) to be for mathematics and physics. The mathematics and physics culture in Germany was booming and this boom was nowhere more pronounced than in Göttingen in 1926. In that year, Mahler found himself working in an illustrious group of applied mathematicians. Indeed, in 1926, the famous American applied mathematician Norbert Wiener received a Guggenheim fellowship to work with Max Born in Göttingen and then to travel on to work with Niels Bohr in Copenhagen. In that year, Born’s assistant was Werner Heisenberg, who would follow Wiener to Copenhagen and there develop what would later become his famous uncertainty principle. It is in this setting that, while in Göttingen, Wiener was given an (unpaid) assistant—a (barely) 23-year-old Kurt Mahler! Collectively, Wiener [24] and Mahler [M1] produced a two-part series of papers entitled, “The spectrum of an array and its application to the study of the translational properties of a simple class of arithmetical functions.” Wiener describes the purpose of the series in the first paragraphs of his part. “The purpose of the present paper is to extend the spectrum theory already developed by the author in a series of papers to the harmonic analysis of functions only defined for a denumerable set of arguments—arrays, as we shall call them—and the application of this theory to the study of certain power series admitting the unit circle as an essential boundary.”
- Subject
- Diophantine approximation; algebraic number thory; p-adic analysis; distribution modulo 1
- Identifier
- http://hdl.handle.net/1959.13/1451001
- Identifier
- uon:44072
- Identifier
- ISSN:1431-0635
- Language
- eng
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