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Loo-Keng Hua Selected Papers

Loo-Keng Hua
Publication Date: 
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Springer Collected Works in Mathematics
[Reviewed by
Allen Stenger
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Loo-Keng Hua (1910–1985) was a versatile Chinese mathematician who worked primarily in number theory. Hua was mostly self-taught in mathematics; he had only 9 years of schooling altogether, and did not have a college or university degree until late in his career, in 1979, when he received an honorary doctorate from the University of Nancy. He worked primarily in China, but also held appointments in England, Russia, and the United States. In addition to his research papers, Hua wrote a number of popular works, monographs, and textbooks, mostly in Chinese. One especially notable one is Introduction to Number Theory (Chinese 1957, English translation from Springer in 1982), that is indeed an introduction but also covers a number of interesting advanced topics.

These selecta reprint 48 of his 150 published papers. The present volume is a 2015 unaltered reprint of the 1983 original collection. The papers were selected by Heini Halberstam, and each group of papers has an introduction by a subject matter expert. All but two were originally published in English, and those two appear here in English translation. Hua’s most active research years were the 1940s and 1950s, so most of these papers are at least 60 years old and the subject matter is usually available in newer books.

There are three major groupings of papers in this volume. Number Theory covers his work in the Hardy-Littlewood and Vinogradov circles of ideas and has a lot on Waring’s problem. Algebra and Geometry is primarily about skew fields and modular groups. Function Theory is primarily about functions of several complex variables and owes a great deal to E. Cartan. There is also a brief collection of miscellaneous papers. There is also a long list of real-world problems that Hua worked on in industry as an applied mathematician, but that did not lead to any papers. The collection ends with a complete bibliography of Hua’s publications.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.

Biographical Note (by Heini Halberstam)

Number Theory (introduced by Wang Yuan)

Algebra and Geometry (introduced by Z. X. Wan)

Function Theory (introduced by S. Kung and K. H. Look)

Miscellaneous Applied Mathematics (by Applied Mathematics Group, Academia Sinica)

Loo-Keng Hua: Publications