The Hahn-Banach theorem is one of the most fundamental theorems in the functional analysis theory. This theorem is well known in the case where the range space is the real number system as follows. Let p be a sublinear mapping from a vector space X into the real number system R, Y a subspace of X, and q a linear mapping from Y into R such that q ≤ p on Y. Then there exists a linear mapping g fr...

We discuss a trinity, i.e., three distinct expressions, of the Borcherds Φ-function on the analogy of the trinity of the Dedekind η-function.

A complete classification is obtained for all second-order linear recurring sequences uniformly distributed modulo an ideal of a Dedekind domain.

Elliptic Dedekind sums were introduced by R. Sczech as generalizations of classical to complex lattices. We show that for any lattice with real $j$-invariant, the values suitably normalized elliptic are dense in num

We investigate when an exact functor F ∼= − ⊗Λ MΓ : mod-Λ → mod-Γ which induces a stable equivalence is part of a stable equivalence of Morita type. If Λ and Γ are finite dimensional algebras over a field k whose semisimple quotients are separable, we give a necessary and sufficient condition for this to be the case. This generalizes a result of Rickard’s for self-injective algebras. As a corol...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. In this paper we concentrate on the issues specific to the case when G is trivial, so the action reduces to the action of a Lie group G. For G simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result b...

Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b − 4ac = d, a > 0, gcd(a, b, c) = 1. The value of |η ( (b + √ d)/2a ) | is determined explicitly, where η(z) is Dedekind’s eta function η(z) = e ∞ ∏ m=1 (1− e) ( im(z) > 0 ) .