Arithmetic of Hermitian forms
Goro Shimura
Department of Mathematics Princeton University Princeton NJ 08544-1000 USA
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Abstract
We investigate the following two problems on a hermitian form over an algebraic number field: (1) classification of over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author's previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation , where and represent hermitian forms. We connect the number of such modulo a group of units with the class number and mass of the unitary group of a form such that .
Cite this article
Goro Shimura, Arithmetic of Hermitian forms. Doc. Math. 13 (2008), pp. 739–774
DOI 10.4171/DM/258