We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by reducing them to Kawashima relation.

Keywords: Hurwitz–Lerch Zeta function Lipschitz–Lerch Zeta function Lerch Zeta function Hurwitz Zeta function Riemann Zeta function Legendre chi function Bernoulli polynomials Bernoulli numbers Discrete Fourier transform a b s t r a c t It is shown that there exists a companion formula to Srivastava's formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bern...

We obtain formulas for the spectral zeta function of the Laplacian on symmetric finitely ramified fractals, such as the Sierpiński gasket, and a fractal Laplacian on the interval. These formulas contain a new type of zeta function associated with a polynomial (rational functions also can appear in this context). It is proved that this zeta function has a meromorphic continuation to a half plain...

The use of elliptic and hyperelliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test whether the Jacobian – over a finite field Fq – of a hyperelliptic curve of the form Y 2 = X + aX + bX (with a, b ∈ Fq) has a large prime factor. His approach is to obtain candidates for the ...

Two dimensional, time-independent and time-dependent electro-osmotic flows driven by a uniform electric field in a closed rectangular cavity with uniform and nonuniform zeta potential distributions along the cavity’s walls are investigated theoretically. First, we derive an expression for the one-dimensional velocity and pressure profiles for a flow in a slender cavity with uniform (albeit poss...

In 1918 G. Hardy and J. Littlewood proved an asymptotic estimate for the Second moment of the modulus of the Riemann zeta-function on the segment [1/2,1/2+iT] in the complex plane, as T tends to infinity. In 1926 Ingham proved an asymptotic estimate for the fourth moment. However, since Ingham’s result, nobody has proved an asymptotic formula for any higher moment. Recently J. Conrey and A. Gho...

Bioengineered spider silks are a biomaterial with great potential for applications in biomedicine. They are biocompatible,biodegradable and can self-assemble into films, hydrogels, scaffolds, fibers, capsules and spheres. A novel, tag-free, bioengineered spider silk named MS2(9x) was constructed. It is a 9-mer of the consensus motif derived from MaSp2-the spidroin of Nephila clavipes dragline s...