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Diophantine analysis is an extremely active field in number theory because of its many open problems and conjectures. Requiring only a basic understanding of number theory, Diophantine Analysis is built around the detailed theory of continued fractions and features many applications and examples. The author includes many new topics related to discrete mathematics, such as factoring large integers, error-free computing, and factoring polynomials. He also provides problem sections at the end of each chapter, where open problems are discussed along with other new topics, such as Apry's proof of...

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann's hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors' approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.