Geodesic
Arithmetic of Hermitian forms
Documenta mathematica, Tome 13 (2008), pp. 739-774.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We investigate the following two problems on a hermitian form $\Phi$ over an algebraic number field: (1) classification of $\Phi$ 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 $\x\Phi\cdot\tr \x^{\r}=\Psi$, where $\Phi$ and $\Psi$ represent hermitian forms. We connect the number of such $\x $ modulo a group of units with the class number and mass of the unitary group of a form $\Th$ such that $\Phi\approx\Psi\oplus\Th$.
Classification : 11E39, 11E41, 11D09 
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     author = {Shimura, Goro},
     title = {Arithmetic of {Hermitian} forms},
     journal = {Documenta mathematica},
     pages = {739--774},
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     volume = {13},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a4/}
}
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Shimura, Goro. Arithmetic of Hermitian forms. Documenta mathematica, Tome 13 (2008), pp. 739-774. http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a4/