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...

Syntrophins are scaffold proteins that regulate the subcellular localization of diacylglycerol kinase zeta (DGK-zeta), an enzyme that phosphorylates the lipid second-messenger diacylglycerol to yield phosphatidic acid. DGK-zeta and syntrophins are abundantly expressed in neurons of the developing and adult brain, but their function is unclear. Here, we show that they are present in cell bodies,...

The chemokine stromal cell-derived factor-1 (SDF-1) and its receptor, CXCR4, play a major role in migration, retention, and development of hematopoietic progenitors in the bone marrow. We report the direct involvement of atypical PKC-zeta in SDF-1 signaling in immature human CD34(+)-enriched cells and in leukemic pre-B acute lymphocytic leukemia (ALL) G2 cells. Chemotaxis, cell polarization, an...

It is well known that the Riemann Zeta function ζ ( p ) = ∑∞n=1 1/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑∞ n=1 1/ ( 4n2−α2)p . In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form repre...

The history of problems of evaluation of series associated with the Riemann Zeta function can be traced back to Christian Goldbach (1690–1764) and Leonhard Euler (1707–1783). Many di¤erent techniques to evaluate various series involving the Zeta and related functions have since then been developed. The authors show how elegantly certain families of series involving the Zeta function can be eval...

Recently, Storm [10] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm’s Theorem. Furthermore, we generalize the...

Recently, Storm [8] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi...

Sharp bounds are obtained for expressions involving Zeta and related functions at a distance of one apart. Since Euler discovered in 1736 a closed form expression for the Zeta function at the even integers, a comparable expression for the odd integers has not been forthcoming. The current article derives sharp bounds for the Zeta, Lambda and Eta functions at a distance of one apart. The methods...

Abstract. Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q → 1. Here, we discuss the sum formula for multiple q-zeta values, and provide a self-contained proof. As a consequence, we also derive a q-analog of Euler’s ...