By Hiroyuki Yoshida

The primary subject of this ebook is an invariant hooked up to an excellent category of a unconditionally genuine algebraic quantity box. This invariant offers us with a unified figuring out of sessions of abelian kinds with advanced multiplication and the Stark-Shintani devices. this can be a new perspective, and the e-book includes many new effects on the topic of it. to put those leads to right point of view and to provide instruments to assault unsolved difficulties, the writer supplies systematic expositions of primary subject matters. hence the publication treats the a number of gamma functionality, the Stark conjecture, Shimura's interval image, absolutely the interval image, Eisenstein sequence on $GL(2)$, and a restrict formulation of Kronecker's variety. The dialogue of every of those subject matters is more advantageous by means of many examples. the vast majority of the textual content is written assuming a few familiarity with algebraic quantity idea. approximately thirty difficulties are integrated, a few of that are rather tough. The publication is meant for graduate scholars and researchers operating in quantity idea and automorphic kinds.

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