{"product_id":"9783034801652","title":"Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms","description":"\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\u003e\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\u003cp\u003e\u003c\/p\u003e","brand":"Springer Basel","offers":[{"title":"Default Title","offer_id":47034995605744,"sku":"9783034801652","price":99.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9783034801652_p0.jpg?v=1763711510","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783034801652","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}