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On the youthful writings of Louis J. Mordell on the Diophantine equation \(y^2-k=x^3\). (English) Zbl 1420.11004

Summary: This article examines the research of Louis J. Mordell on the Diophantine equation \(y^2-k=x^3\) as it appeared in one of his first papers, published in 1914. After presenting a number of elements relating to Mordell’s mathematical youth and his (problematic) writing, we analyze the 1914 paper [Proc. Lond. Math. Soc. (2) 13, 60–80 (1914; JFM 44.0230.03)] by following the three approaches he developed therein, respectively, based on the quadratic reciprocity law, on ideal numbers, and on binary cubic forms. This analysis allows us to describe many of the difficulties in reading and understanding Mordell’s proofs, difficulties which we make explicit and comment on in depth.

MSC:

11-03 History of number theory
01A60 History of mathematics in the 20th century
11D25 Cubic and quartic Diophantine equations
11G05 Elliptic curves over global fields

Biographic References:

Mordell, Louis Joel

Citations:

JFM 44.0230.03
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Full Text: DOI

References:

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