# Volume 09 (2005) No. 2

## Volume 09 (2005) No. 2

### Riemann and his zeta function

Elena A. Kudryavtseva, Filip Saidak, and Peter Zvengrowski

**Abstract:**

An exposition is given, partly historical and partly mathematical, of the Riemann zeta function $\zeta(s)$ and the associated Riemann hypothesis. Using techniques similar to those of Riemann, it is shown how to locate and count non-trivial zeros of $\zeta(s)$. Relevance of these investigations to the theory of the distribution of prime numbers is discussed.

### Secondary operations in $K$-theory and the generalized vector field problem (revisited)

Jesús González and Maurilio Velasco-Fuentes

**Abstract:**

We describe detailed calculations of secondary operations in complex $K$-theory leading to results on the generalized vector field problem for projective spaces. The method was originally published by Feder and Iberkleid in 1977. Our interest in understanding those ideas rests on the possibility to extend their results to the case of $2^e$-torsion lens spaces in order to analyze the torsion's role in the generalized vector field problem for these manifolds.

### Complete intersection toric ideals of oriented graphs

Enrique Reyes

**Abstract:**

Let $G$ be a connected simple graph. We prove the existence of an orientation $\mathcal{O}$ of $G$ such that the toric ideal asociated to the digraph $\mathcal{D}=(G,\mathcal{O})$ is a complete intersection.