A note on excellent forms

A note on quadratic forms

We extend an interesting theorem of Yuan [12] for two quadratic forms to three matrices. Let C1, C2, C3 be three symmetric matrices in <n×n , if max{xT C1x, xT C2x, xT C3x} ≥ 0 for all x ∈ <n , it is proved that there exist ti ≥ 0 (i = 1, 2, 3) such that ∑3 i=1 ti = 1 and ∑3 i=1 ti Ci has at most one negative eigenvalue.

A note on bilinear forms

A Note on Hermitian Forms

In this note we effect a reduction of the theory of hermitian forms of two particular types (coefficients in a quadratic field or in a quaternion algebra with the usual anti-automorphism) to that of quadratic forms. The main theorem (§2) enables us to apply directly the known results on quadratic forms. This is illustrated in the discussion in §3 of a number of special cases. Let <£ be an arbit...

A Note on Maass-Jacobi Forms

In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.

A note on Clifford-Klein forms

We consider the problem of finding Clifford-Klein forms in a class of homogeneous spaces determined by inclusions of real Lie algebras of a special type which we call strongly regular. This class of inclusions is described in terms of their Satake diagrams. For example, the complexifications of such inclusions contain the class of subalgebras generated by automorphisms of finite order. We show ...