{"product_id":"pseudodifferential-analysis-automorphic-distributions-in-the-plane-and-modular-forms-paperback","title":"Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eAndré Unterberger\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ePseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R\u003csup\u003e2\u003c\/sup\u003e into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of \u003ci\u003eg\u003c\/i\u003e-transforms, for \u003ci\u003eg E SL\u003c\/i\u003e(2\u003ci\u003e;\u003c\/i\u003eZ), of some initial function, say in \u003ci\u003eS\u003c\/i\u003e(R\u003csup\u003e2\u003c\/sup\u003e), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip.\u003c\/p\u003e \u003cp\u003eThe book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ePseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in \u003cb\u003eR\u003c\/b\u003e\u003csup\u003e2\u003c\/sup\u003e into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of \u003ci\u003eg\u003c\/i\u003e-transforms, for \u003ci\u003eg \u003c\/i\u003eÎ\u003ci\u003e SL\u003c\/i\u003e(2\u003ci\u003e;\u003c\/i\u003e\u003cb\u003eZ\u003c\/b\u003e), of some initial function, say in \u003ci\u003eS\u003c\/i\u003e(\u003cb\u003eR\u003c\/b\u003e\u003csup\u003e2\u003c\/sup\u003e), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip.\u003c\/p\u003e \u003cp\u003eThe book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 300\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.7 x 9.5 x 6.6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 06, 2011\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704861323571,"sku":"9783034801652","price":96.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/dEdvTzZjV0x6OWgvNjFlNHI3eWxYdz09.webp?v=1763366299","url":"https:\/\/www.vysn.com\/en-ca\/products\/pseudodifferential-analysis-automorphic-distributions-in-the-plane-and-modular-forms-paperback","provider":"VYSN","version":"1.0","type":"link"}