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Book review

Author(s) Holzapfel, R.P.
Title Geometry and Arithmetic Around Euler Partial Differential Equations
Publisher D.Reidel Publishing Company
Year of publication 1986

This book focuses on the Euler-Picard system of partial differential equations <formula>, where <formula> denotes a holomorphic function, and l, m are natural numbers such that <formula>.

Using modern mathematical language, the author gives the comprehensive investigation of the Euler-Picard system. The volume contains three chapters. Chapter 0, Introduction, presents the historical developments, results and methods elucidated in the book. Chapter 1, The Picard Curve Family and Eisenstein Lattices of the Complex Unit Ball, supplies the results concerning with the classification of the complex surfaces. Chapter 2, The Gauss - Manin Connection of Cycloelliptic Curve Families, gives the complete solution of the Euler-Picard system.

This text is intended for researchers and pool-graduate students with interest in algebraic geometry, automorphic forms theory, monodromy groups of differential equations. In order to make the best use of the book there is index.

All in all, Geometry and Arithmetic Around Euler Partial Differential Equations, examines classical topics from the standpoint of the modern mathematics and I can recommend its purchace for students, experts and libraries alike.