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This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.

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Bring the soothing energy of nature into your home with this floral print. The light green floral silhouettes sport both a textural and pearlescent finish. Softly offset by the distressed light grey backdrop with raised ink detailing. Riemann is an unpasted, vinyl on paper wallpaper.

Color/pattern: riemann cream floral Design details: add neutral texture to your home with this compelling trail wallpaper. each floral silhouette is detailed with textural pearlescence, the distressed cream backdrop added another layer of dimension to the monotone design. riemann is an unpasted, vinyl on paper wallpaper. unpasted vinyl material; 10.4-in repeat, drop match; scrubbable and peelable; 20.9-in by 33-ft long roll; covers about 57.5 square feet Measures 20.9in x 396in x 0.025in Vinyl Wipe clean with a damp cloth Imported

Color/pattern: riemann green floral Design details: bring the soothing energy of nature into your home with this floral print. the light green floral silhouettes sport both a textural and pearlescent finish. softly offset by the distressed light grey backdrop with raised ink detailing. riemann is an unpasted, vinyl on paper wallpaper. unpasted vinyl material; 10.4-in repeat, drop match; scrubbable and peelable; 20.9-in by 33-ft long roll; covers about 57.5 square feet Measures 20.9in x 396in x 0.025in Vinyl Wipe clean with a damp cloth Imported

Color/pattern: riemann beige floral Design details: bring floral elegance to your home with this natural and neutral design. each bloom's silhouette is filled with a textural beige and imprinted against distressed cream backdrop with raised ink detailing. riemann is an unpasted, vinyl on paper wallpaper. unpasted vinyl material; 10.4-in repeat, drop match; scrubbable and peelable; 20.9-in by 33-ft long roll; covers about 57.5 square feet Measures 20.9in x 396in x 0.025in Vinyl Wipe clean with a damp cloth Imported

Bring floral elegance to your home with this natural and neutral design. Each bloom's silhouette is filled with a textural beige and imprinted against distressed cream backdrop with raised ink detailing. Riemann is an unpasted, vinyl on paper wallpaper.

Enjoy traditional elegance with this floral silhouette print. Trails of silver leaves and flowers are accented by metallic raised inks and imprinted against the distressed off-white backdrop. Riemann is an unpasted, vinyl on paper wallpaper. Color: Gray.

Color/pattern: riemann silver floral Design details: enjoy traditional elegance with this floral silhouette print. trails of silver leaves and flowers are accented by metallic raised inks and imprinted against the distressed off-white backdrop. riemann is an unpasted, vinyl on paper wallpaper. unpasted vinyl material; 10.4-in repeat, drop match; scrubbable and peelable; 20.9-in by 33-ft long roll; covers about 57.5 square feet Measures 20.9in x 396in x 0.025in Vinyl Wipe clean with a damp cloth Imported

Add neutral texture to your home with this compelling trail wallpaper. Each floral silhouette is detailed with textural pearlescence, the distressed cream backdrop added another layer of dimension to the monotone design. Riemann is an unpasted, vinyl on paper wallpaper. Color: Beige.

The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ... Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions. The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ... Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions. The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

Spine is cracked, cocked, and shaken but secure. Cover edges are slightly worn. Text block is tanned, but legibility is not affected. Front free end paper has previous seller's price sticker. Front free end paper and cover page are torn along spine, but are secure. Back end papers are lightly foxed. Inside is unmarked.

"A thorough and easily accessible account." — MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estimates, the distribution of primes, the Dirichlet divisor problem and various other divisor problems, and Atkinson's formula for the mean square. End-of-chapter notes supply the history of each chapter's topic and allude to related results not covered by the book. 1985 edition.

The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many other fields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics. This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind. Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved. Following this section, the remainder of the text illustrates various facets of the more advanced theory.

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High resolution upwind and centred methods are a mature generation of computational techniques applicable to a range of disciplines, Computational Fluid Dynamics being the most prominent. This book gives a practical presentation of this class of techniques.