We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to analyse. We prove that reduced zeta functions are multiplicative under certain conditions and investigate which reduced zeta functions have functional equations.

To probe Pol zeta functions in vivo via its error signature, here we report the properties of Saccharomyces cerevisiae Pol zeta in which phenyalanine was substituted for the conserved Leu-979 in the catalytic (Rev3) subunit. We show that purified L979F Pol zeta is 30% as active as wild-type Pol zeta when replicating undamaged DNA. L979F Pol zeta shares with wild-type Pol zeta the ability to per...

The occurrence of Hb H hydrops fetalis is reported for the first time. The mother has zeta-alpha thalassemia 1 (zeta zeta alpha alpha/----) and the father has non-deletion alpha thalassemia [zeta zeta alpha alpha/zeta zeta (alpha alpha)T]. The complete deletion of the zeta alpha cluster on one chromosome was confirmed by quantitation of alpha and zeta gene numbers, the normal alpha and zeta gen...

Protein kinase C-zeta (PKC-zeta) is a serine/threonine kinase downstream from phosphatidylinositol 3-kinase in insulin signaling pathways. However, specific substrates for PKC-zeta that participate in the biological actions of insulin have not been reported. In the present study, we identified insulin receptor substrate-1 (IRS-1) as a novel substrate for PKC-zeta. Under in vitro conditions, wil...

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto’s factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the...

Holomorphic maps between complex manifolds have many properties which distinguish them among general smooth maps. Consider, for example, the case of a map between Riemann surfaces. A holomorphic map is represented locally, in suitable co-ordinates, by one of the models z 7→ z for k ≥ 0. These models are very different from the models of generic smooth maps between surfaces, which are, in additi...

We give a new and bijective proof for the formula of the growth function of the positive braid monoid with respect to Artin generators.

Let f = (f1, . . . , fl) : U → Kl, with K = R or C, be a K-analytic mapping defined on an open set U ⊆ Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f , Φ) in terms of a log-principalization of the ideal If = (f1, . . . , fl). When f is a non-degenerate mapping, we give an explicit...

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2 + iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riem...

In 2009, Cooper presented an infinite family of pairs of graphs which were conjectured to have the same Ihara zeta function. We give a proof of this result by using generating functions to establish a one-to-one correspondence between cycles of the same length without backtracking or tails in the graphs Cooper proposed. Our method is flexible enough that we are able to generalize Cooper’s graph...