Arithmetic of Hermitian Forms

  title={Arithmetic of Hermitian Forms},
  author={Goro Shimura},
We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ 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 ξΦ · ξ = Ψ , where Φ and Ψ represent hermitian forms. We connect the number of such ξ modulo a group of units with the class number and mass… CONTINUE READING

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