Complex conjugate pairs in stationary Sturmian eigenstates

Complex Conjugate Pairs in Stationary Sturmians

Sturmian eigenstates specified by stationary scattering boundary conditions are particularly useful in contexts such as forming simple separable two nu-cleon t matrices, and are determined via solution of generalised eigenvalue equation using real and symmetric matrices. In general, the spectrum of such an equation may contain complex eigenvalues. But to each complex eigenvalue there is a corre...

On primitives and conjugate harmonic pairs in Hermitean Clifford analysis

The notion of a conjugate harmonic pair in the context of Hermitean Clifford analysis is introduced as a pair of specific harmonic functions summing up to a Hermitean monogenic function in an open region Ω of C. Under certain geometric conditions on Ω the conjugate harmonic to a given specific harmonic is explicitly constructed and the potential or primitive of a Hermitean monogenic function is...

Non-homeomorphic Conjugate Complex Varieties

We present a method to produce examples of non-homeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs.

Ramanujan-type partial theta identities and conjugate Bailey pairs

Residual identities of Ramanujan-type partial theta identities are tailor-made for producing conjugate Bailey pairs. This is carried out for partial theta identities in Ramanujan’s lost notebook, a number of the partial theta identities of Warnaar, and for some new ones as well.

Powers in Sturmian sequences