{"product_id":"commensurabilities-among-lattices-in-pu-pierre-r-deligne-9780691000961","title":"Commensurabilities Among Lattices in Pu (1, N). (Am-132), Volume 132","description":"\u003cp\u003eThe first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, \u003ci\u003etwists\u003c\/i\u003e of hypergeometric functions in \u003ci\u003en\u003c\/i\u003e-variables. These are treated as an (\u003ci\u003en\u003c\/i\u003e+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of \u003ci\u003en\u003c\/i\u003e+3 tuples of distinct points on the projective line \u003ci\u003eP\u003c\/i\u003e modulo, the diagonal section of Auto \u003ci\u003eP\u003c\/i\u003e=\u003ci\u003em\u003c\/i\u003e. For \u003ci\u003en\u003c\/i\u003e=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of \u003ci\u003ePU\u003c\/i\u003e(1, \u003ci\u003en\u003c\/i\u003e). \u003cp\u003e\u003c\/p\u003e The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in \u003ci\u003ePU\u003c\/i\u003e(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors \"at infinity\" permits one to prove generalizations in \u003ci\u003en\u003c\/i\u003e-variables of the Kummer identities for \u003ci\u003en\u003c\/i\u003e-1 involving quadratic and cubic changes of the variable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Pierre R. Deligne,George Daniel Mostow\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691000964\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691000961\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/12\/1993\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 218\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.60lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.22h x 6.08w x 0.52d","brand":"Pierre R. Deligne","offers":[{"title":"Paperback","offer_id":48153082691839,"sku":"9780691000961","price":104.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_a3c95d27-5195-4204-a8db-32b0f39f96bf.jpg?v=1770781164","url":"https:\/\/www.whiterainbookhouse.com\/products\/commensurabilities-among-lattices-in-pu-pierre-r-deligne-9780691000961","provider":"WR Book House","version":"1.0","type":"link"}