By Henryk Iwaniec

Automorphic kinds are one of many critical themes of analytic quantity concept. actually, they take a seat on the confluence of study, algebra, geometry, and quantity concept. during this booklet, Henryk Iwaniec once more screens his penetrating perception, strong analytic concepts, and lucid writing sort. the 1st version of this quantity used to be an underground vintage, either as a textbook and as a revered resource for effects, principles, and references. The book's acceptance sparked a becoming curiosity within the mathematical group to deliver it again into print. The AMS has replied that decision with the ebook of this moment variation. within the publication, Iwaniec treats the spectral thought of automorphic kinds because the research of the gap $L^2 (H\Gamma)$, the place $H$ is the higher half-plane and $\Gamma$ is a discrete subgroup of volume-preserving alterations of $H$. He combines numerous innovations from analytic quantity concept. one of the subject matters mentioned are Eisenstein sequence, estimates for Fourier coefficients of automorphic types, the speculation of Kloosterman sums, the Selberg hint formulation, and the speculation of small eigenvalues. Henryk Iwaniec used to be presented the 2002 AMS Cole Prize for his basic contributions to analytic quantity concept. additionally to be had from the AMS by means of H. Iwaniec is themes in Classical Automorphic kinds, quantity 17 within the Graduate stories in arithmetic sequence. The ebook is designed for graduate scholars and researchers operating in analytic quantity idea.

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