We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous n th-order scalar ordinary diierential equations with coeecients being elliptic functions (associated with a common period lattice) to linear homogeneous rst-order n n systems. In particular, the qualitative structure of the general solution in terms of elliptic and exponential functions, ...

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n×n matrix a = (aα) , i, α = 1, . . . , n (with noncommuting entries) and by rational functions of n commuting elements qi satisfying n ∏ i=1 qi = 1, qaα = a j αq pi+δ j i− 1 n . We study a generalization of the Fock space (F) representation of A for generic q (q not a root of uni...

We study the 2k th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes & Keating for the Riemann zeta function. This allows us to recover conjectures for the moments based on random matrix models, incorporating t...

Abstract. We study the 2k-th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta-function. This allows us to recover conjectures for the moments based on random matrix models, inc...

In this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. We present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number.

The subject of this thesis is quantum groups and quantum algebras at a root of unity. After an introductory chapter, I set up my notation in chapter 2. The rest of the thesis is presented in three parts. In part I, quantum matrix groups and quantum enveloping algebras are discussed. In chapter 3, I present two well-known 2 × 2 matrix quantum groups, including their coaction on the quantum plane...

We study the 2k th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes & Keating for the Riemann zeta function. This allows us to recover conjectures for the moments based on random matrix models, incorporating t...

In this article we apply a formula for the n-th power of a 3×3 matrix (found previously by the authors) to investigate a procedure of Khovanskii’s for finding the cube root of a positive integer. We show, for each positive integer α, how to construct certain families of integer sequences such that a certain rational expression, involving the ratio of successive terms in each family, tends to α....

Efficient computation of r-th root in Fq has many applications in computational number theory and many other related areas. We present a new r-th root formula which generalizes Müller’s result on square root, and which provides a possible improvement of the CipollaLehmer type algorithms for general case. More precisely, for given r-th power c ∈ Fq, we show that there exists α ∈ Fqr such that Tr...