Results 1 to 10 of about 2,325,357 (271)

The lifting of an exponential sum to a cyclic algebraic number field of prime degree

, 1998
Let E be a cyclic algebraic number field of prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.
Y. Ye
semanticscholar   +1 more source

The Markoff spectrum of an algebraic number field

Journal of the Australian Mathematical Society, 1978
The Markoff spectrum of an algebraic number field is defined and it is proved that the spectrum of Q(✓5) is not discrete.
A. Woods
semanticscholar   +1 more source

On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices

Abstract and Applied Analysis, 2014
Circulant matrices have important applications in solving various differential equations. The level-k scaled factor circulant matrix over any field is introduced.
Zhaolin Jiang
doaj   +1 more source

On the Genus number of Algebraic groups [PDF]

arXiv, 2013
We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action of these groups on their Lie algebras. We also prove that the genus number of a connected reductive algebraic group
arxiv  

Multilayer tube impedance and external radiation

Physical Review Special Topics. Accelerators and Beams, 2008
The paper describes a method for calculating the longitudinal and transverse impedances of the laminated round pipe with many layers of different materials. The charge is moving along the pipe axis with arbitrary constant velocity.
M. Ivanyan, E. Laziev, V. Tsakanov, A. Vardanyan, S. Heifets, A. Tsakanian   +5 more
doaj   +1 more source

Notes on the Theory of Algebraic Numbers [PDF]

arXiv, 2015
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag, 1981 (English translation by G.
arxiv  

Discrete Cartesian Coordinate Transformations: Using Algebraic Extension Methods

Applied Sciences
It is shown that it is reasonable to use Galois fields, including those obtained by algebraic extensions, to describe the position of a point in a discrete Cartesian coordinate system in many cases. This approach is applicable to any problem in which the
Aruzhan Kadyrzhan, Dinara Matrassulova, Yelizaveta Vitulyova, Ibragim Suleimenov   +3 more
doaj   +1 more source

A residue scalar product for algebraic function fields over a number field [PDF]

arXiv, 1999
In 1952 Peter Roquette gave an arithmetic proof of the Riemann hypothesis for algebraic function fields of a finite constants field, which was proved by Andr\'e Weil in 1940. The construction of Weil's scalar product is essential in Roquette's proof. In this paper a scalar product for algebraic function fields over a number field is constructed which ...
arxiv  

Linear Independence of 𝑞-Logarithms over the Eisenstein Integers

International Journal of Mathematics and Mathematical Sciences, 2010
For fixed complex 𝑞 with |𝑞|>1, the 𝑞-logarithm 𝐿𝑞 is the meromorphic continuation of the series ∑𝑛>0𝑧𝑛/(𝑞𝑛−1),|𝑧|1,𝑐≠𝑞,𝑞2,𝑞3,…. In 2004, Tachiya showed that this is true in the Subcase 𝐾=ℚ, 𝑞∈ℤ, 𝑐=−1, and the present authors extended this result to ...
Peter Bundschuh, Keijo Väänänen
doaj   +1 more source

Multi-terminal thermoelectric transport in a magnetic field: bounds on Onsager coefficients and efficiency

New Journal of Physics, 2013
Thermoelectric transport involving an arbitrary number of terminals is discussed in the presence of a magnetic field breaking time-reversal symmetry within the linear response regime using the Landauer–Büttiker formalism.
Kay Brandner, Udo Seifert
doaj   +1 more source