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An introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects. Each chapter covers both subjects, and a table is provided at the end of each chapter to indicate the correspondence of theorems.

Diophantine approximation. --- Nevanlinna theory. --- Functions, Meromorphic --- Value distribution theory --- Approximation, Diophantine --- Approximation theory --- Diophantine analysis

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This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavor. In particular, estimates for the number of solutions of diophantine equations as well as results concerning congruences and polynomials are established. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and to discrepancy theory. The articles are based on lectures given at a conference at the Erwin Schr6dinger Institute in Vienna in 2003, in which many leading experts in the field of diophantine approximation participated. The editors are very grateful to the Erwin Schr6dinger Institute and to the FWF (Austrian Science Fund) for the financial support and they express their particular thanks to Springer-Verlag for the excellent cooperation. Robert E Tichy Diophantine Approximation H. E Schlickewei et al. , Editors 9 Springer-Verlag 2008 THE MATHEMATICAL WORK OF WOLFGANG SCHMIDT Hans Peter Schlickewei Mathematik Informatik, und Philipps-Universitiit Hans-Meerwein-Strasse, Marburg, 35032 Marburg, Germany k. Introduction Wolfgang Schmidt's mathematical activities started more than fifty years ago in 1955. In the meantime he has written more than 180 papers - many of them containing spectacular results and breakthroughs in different areas of number theory.

Diophantine approximation --- Approximation, Diophantine --- Approximation theory --- Diophantine analysis --- Algebra. --- Computer science --- Number theory. --- Computational Mathematics and Numerical Analysis. --- Number Theory. --- Mathematics. --- Number study --- Numbers, Theory of --- Algebra --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Mathematical analysis --- Computer mathematics.

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This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.

Diophantine approximation. --- Diophantine equations. --- Diophantine analysis. --- Indeterminate analysis --- Diophantic equations --- Equations, Diophantic --- Equations, Diophantine --- Equations, Indefinite --- Equations, Indeterminate --- Indefinite equations --- Indeterminate equations --- Approximation, Diophantine --- Mathematics. --- Number theory. --- Number Theory. --- Number theory --- Forms, Quadratic --- Diophantine analysis --- Approximation theory --- Number study --- Numbers, Theory of --- Algebra

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The lifeblood of the global economy, information has become a source of growing risk as more firms maintain information online. With risks now fueled by sophisticated, organized, malicious groups, information security requires not only technology, but a clear understanding of potential risks, decision-making behaviors, and metrics for evaluating business and policy options. Managing Information Risk and the Economics of Security, an edited volume contributed by well-established researchers in the field worldwide, presents the latest research on economics driving both the risks and the solutions. Covering the implications of policy within firms and across countries, this volume provides managers and policy makers with new thinking on how to manage risk. Managing Information Risk and the Economics of Security is designed for managers, policy makers, and researchers focusing on economics of information security, as well as for advanced-level students in computer science, business management and economics. .

Algebraic number theory. --- Diophantine approximation. --- Diophantine approximation --- 511.5 --- Approximation, Diophantine --- Diophantine analysis --- Diophantine equations --- 511.5 Diophantine equations --- Biometry --Congresses. --- Computer science. --- Business. --- Management science. --- Computer communication systems. --- Computer security. --- Data encryption (Computer science). --- Economics. --- Computer Science. --- Systems and Data Security. --- Business and Management, general. --- Computer Communication Networks. --- Data Encryption. --- Economic Systems. --- Algebraic number theory --- Approximation theory --- Number theory --- Business enterprises --- Computer security --- Information resources management --- Risk management. --- Computer networks --- Security measures --- Economic aspects. --- Insurance --- Management --- Corporations --- Information resource management --- Information systems management --- IRM (Information resources management) --- Management information systems --- Computer privacy --- Computer system security --- Computer systems --- Computers --- Cyber security --- Cybersecurity --- Electronic digital computers --- Protection of computer systems --- Security of computer systems --- Data protection --- Security systems --- Hacking --- Business organizations --- Businesses --- Companies --- Enterprises --- Firms --- Organizations, Business --- Business --- Protection --- Cryptology. --- Political Economy/Economic Systems. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Cryptography --- Trade --- Economics --- Commerce --- Industrial management --- Economic policy. --- Economic nationalism --- Economic planning --- National planning --- State planning --- Planning --- National security --- Social policy --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Quantitative business analysis --- Problem solving --- Operations research --- Statistical decision --- Distributed processing --- Approximation diophantienne