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Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":36053767389341,"sku":"9781107499430","price":24.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781107499430.jpg?v=1599565803"},{"product_id":"transcendental-number-theory","title":"Transcendental Number Theory","description":"First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43411222135023,"sku":"9781009229944","price":29.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781009229944i.jpg?v=1664188756"},{"product_id":"o-minimality-and-diophantine-geometry","title":"O-Minimality and Diophantine Geometry","description":"This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43411629670639,"sku":"9781107462496","price":26.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781107462496i.jpg?v=1664194588"},{"product_id":"auxiliary-polynomials-in-number-theory","title":"Auxiliary Polynomials in Number Theory","description":"This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from number theory to algebraic geometry.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43411759923439,"sku":"9781107061576","price":123.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781107061576i.jpg?v=1664197075"},{"product_id":"applications-of-diophantine-approximation-to-integral-points-and-transcendence","title":"Applications of Diophantine Approximation to Integral Points and Transcendence","description":"This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43411928776943,"sku":"9781108424943","price":106.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108424943i.jpg?v=1664199156"},{"product_id":"modern-analysis-of-automorphic-forms-by-example-volume-1","title":"Modern Analysis of Automorphic Forms By Example: Volume 1","description":"This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":44073598058735,"sku":"9781107154001","price":66.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781107154001.jpg?v=1694782941"},{"product_id":"modern-analysis-of-automorphic-forms-by-example-volume-2","title":"Modern Analysis of Automorphic Forms By Example: Volume 2","description":"This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. 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With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":44073601433839,"sku":"9781108473842","price":66.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781108473842.jpg?v=1694783087"},{"product_id":"eisenstein-series-and-automorphic-representations","title":"Eisenstein Series and Automorphic Representations","description":"\u003cspan data-mce-fragment=\"1\"\u003eThis introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. 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It first develops essential geometric and number theoretical components to the investigations of arithmetic groups, and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces, and some associated cohomological questions. 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