{"product_id":"the-spectrum-of-hyperbolic-surfaces-nicolas-bergeron-9783319276649","title":"The Spectrum of Hyperbolic Surfaces","description":"\u003cp\u003eThis text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called \"arithmetic hyperbolic surfaces\", the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them.\u003c\/p\u003e \u003cp\u003eAfter an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.\u003c\/p\u003e \u003cp\u003eThe fruit of several graduate level courses at Orsay and Jussieu, \u003ci\u003eThe Spectrum of Hyperbolic Surfaces\u003c\/i\u003e allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Nicolas Bergeron\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3319276646\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783319276649\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/02\/2016\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 370\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.19lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.80d","brand":"Nicolas Bergeron","offers":[{"title":"Paperback","offer_id":43940767596799,"sku":"9783319276649","price":79.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_67d714f1-f5eb-4249-8a41-7ff9f735690f.jpg?v=1681449070","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-spectrum-of-hyperbolic-surfaces-nicolas-bergeron-9783319276649","provider":"WR Book House","version":"1.0","type":"link"}