The main result of this paper gives necessary and sufficient conditions for the ^-primary part S(K)P of the Schur group S (K) to be induced from S (F)p for any subfield F of K where K is contained in Q (εn), under the restriction that εp2 is not in K if p > 2 and n is odd if p~2, where εn is a primitive nth root of unity. Moreover we completely answer the question: "When is SiQiεn + ε-)) induce...

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F .

In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite ...

We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (?1)-enumeration of these lozenge tilings. In the case that a = b = c, we also provide closed formulas for certain...

Let E be an elliptic curve, and let Ln be the Kummer extension generated by a primitive pnth root of unity and a pn-th root of a for a fixed a ∈ Q − {±1}. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over Ln in certain cases. The aim of this note is to explain how some of th...

We consider the use of generalized Ding-Helleseth cyclotomy to design sequences over the finite field of order four. Using generalized cyclotomic classes of order four we obtain the family of balanced sequences of odd period with high linear complexity. Also we present a method of constructing sequences with high linear complexity and arbitrary even period over the finite field of order four. T...

Let K be a cyclic Galois extension of degree p over a field F containing a primitive pth root of unity. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F ) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F )]modules. For these embedding problems we prove conditions on solvability, formulas for explicit construction, and results on au...

Let K be a cyclic Galois extension of degree p over a field F containing a primitive pth root of unity. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F ) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F )]modules. For these embedding problems we prove conditions on solvability, formulas for explicit construction, and results on au...

In 1977 Kervaire and Murthy presented three conjectures regarding K0ZCpn , where Cpn is the cyclic group of order p n and p is a semi-regular prime that is p does not divide h (regular p does not divide the class number h = hh). The Mayer-Vietoris exact sequence provides the following short exact sequence 0 → Vn → PicZCpn → ClQ(ζn−1)× PicZCpn−1 → 0 Here ζn−1 is a primitive p -th root of unity. ...