By Henryk Iwaniec
Automorphic kinds are one of many valuable subject matters of analytic quantity conception. actually, they sit down on the confluence of research, algebra, geometry, and quantity concept. during this e-book, Henryk Iwaniec once more screens his penetrating perception, strong analytic options, and lucid writing kind. the 1st variation of this quantity was once an underground vintage, either as a textbook and as a revered resource for effects, rules, and references. The book's recognition sparked a turning out to be curiosity within the mathematical neighborhood to deliver it again into print. The AMS has spoke back that decision with the booklet of this moment version. within the ebook, 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 modifications of $H$. He combines a variety of strategies from analytic quantity concept. one of the themes mentioned are Eisenstein sequence, estimates for Fourier coefficients of automorphic varieties, the speculation of Kloosterman sums, the Selberg hint formulation, and the speculation of small eigenvalues. Henryk Iwaniec used to be provided the 2002 AMS Cole Prize for his primary contributions to analytic quantity concept. additionally to be had from the AMS through H. Iwaniec is subject matters 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 concept.
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