Problems and Theorems in Analysis II: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry [Paperback]

Four. Functions of One Complex Variable. Special Part.- 1. Maximum Term and Central Index, Maximum Modulus and Number of Zeros.- 2. Schlicht Mappings.- 3. Miscellaneous Problems.- Five. The Location of Zeros.- 1. Rolles Theorem and Descartes Rule of Signs.- 2. The Geometry of the Complex Plane and the Zeros of Polynomials.- 3. Miscellaneous Problems.- Six. Polynomials and Trigonometric Polynomials.- ? 1 (17) Tchebychev Polynomials.- ? 2 (815) General Problems on Trigonometric Polynomials.- ? 3 (1628) Some Special Trigonometric Polynomials.- ? 4 (2938) Some Problems on Fourier Series.- ? 5 (3943) Real Non-negative Trigonometric Polynomials.- ? 6 (4449) Real Non-negative Polynomials.- ? 7 (5061) Maximum-Minimum Problems on Trigonometric Polynomials.- ? 8 (6266) Maximum-Minimum Problems on Polynomials.- ? 9 (6776) The Lagrange Interpolation Formula.- ? 10 (7783) The Theorems of S. Bernstein and A. Markov.- ? 11 (84102) Legendre Polynomials and Related Topics.- ? 12 (103113) Further Maximum-Minimum Problems on Polynomials.- Seven. Determinants and Quadratic Forms.- ? 1 (116) Evaluation of Determinants. Solution of Linear Equations.- ? 2 (1734) Power Series Expansion of Rational Functions.- ? 3 (3543.2) Generation of Positive Quadratic Forms.- ? 4 (4454.4) Miscellaneous Problems.- ? 5 (5572) Determinants of Systems of Functions.- Eight. Number Theory.- 1. Arithmetical Functions.- 2. Polynomials with Integral Coefficients and Integral-Valued Functions.- 3. Arithmetical Aspects of Power Series.- 4. Some Problems on Algebraic Integers.- 5. Miscellaneous Problems.- Nine. Geometric Problems.- ? 1 (125) Some Geometric Problems.- Errata.- ? 1 Additional Problems to Part One.- New Problems in EnglishEdition.- Author Index.- Topics.From the reviews: ... In the past, more of the leading mathematicians proposed and solved problems than today, and there were problem departments in many journals. P?lya and Szego must have combed all of the large problem literaturl““