Abel on Analysis

Papers on abelian and elliptic functions and the theory of series

Kendrick Press, 2007.
xxii + 616 pp. Paperback $100 (ISBN: 0-9793183-0-0).
Hardback $140 (ISBN: 978-0-9793183-0-6).

The mathematician Niels Henrik Abel was born in Norway in August 1802 and died there in April 1829. He produced a remarkable and influential body of work during his short life. In this volume, a selection of Abel's works - those concerned with analysis - is presented in English for the first time. The papers translated cover abelian functions and Abel's theorem, elliptic functions and the foundations of the theory of series. The book also includes Abel's illuminating mathematical correspondence, and the correspondence between two other great contributors to the theory of elliptic functions, Legendre and Jacobi, who were responding to Abel's discoveries as they appeared.

The translator, Philip Horowitz, has also provided a lengthy introduction, notes to the individual papers and a bibliography. He clearly shows how modern algebraic geometry is indebted to the papers translated here.

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