Generalised Kähler structure on $ \mathbb{C}P^2 $ and elliptic functions

Nucleon Structure, Duality and Elliptic Theta Functions

Nucleon structure functions are shown to have a qualitative (or ‘formal’) relation to the classical elliptic theta functions. In particular, θ 1/2 shows a clear resemblance to a non-singlet structure function like xF3. In the appropriate range, the Q2-dependence of the moments of θ 1/2 is in near-quantitative agreement with QCD, and at low-Q2 the moments converge to a common value, as observed ...

Functional Equations and the Generalised Elliptic Genus

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-Höhn by means of a functional equation. Introduction Functional equations provide a common thread to several investigations in mathematics and physics: our focus in this article will particularly be on the areas of topology and integrable systems where it is still unclear whether the threads before us f...

Trigonometric functions, elliptic functions, elliptic modular forms

Synthetic Geometry and Generalised Functions

We review some aspects of the geometry of length spaces and metric spaces, in particular Alexandrov spaces with curvature bounded below and/or above. We then point out some possible directions of research to explore connections between the synthetic approach to Riemannian geometry and some aspects of the approach to non-smooth differential geometry through generalised functions. AMS Mathematics...

Generalised Weber Functions. I

A generalised Weber function is given by wN (z) = η(z/N)/η(z), where η(z) is the Dedekind function and N is any integer; the original function corresponds to N = 2. We classify the cases where some power w N evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formu...