Let K/F be a separable extension. (i) If K = F(α) with αⁿ ∈ F for some n, K/F is said to be a radical extension. (ii) If there exists a sequence of fields F = F₀ ⊆ F₁ ⊆ ... ⊆ F(s) = K so that Fᵢ₊₁ = Fᵢ(αᵢ) with αᵢⁿ⁽ⁱ⁾ ∈ Fᵢ for some nᵢ ∈ N, charF ∧nᵢ for every i, and [Fᵢ₊₁ : Fᵢ] = nᵢ, K/F is said to be a radical tower. In the first part of this work, we present two theorems which give sufficient conditions for a field extension K/F to be radical. In the second part, we present results which provide conditions under which every subfield of a radical tower is also a radical tower.

Thesis (M.S.)--University of North Carolina at Wilmington, 2005. / Includes bibliographical references (Leaf: [104])

Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 112-116). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Oregon State University, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 43-46). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [47]-48).

Let F/F^+ be a quadratic imaginary field extension of a totally real field F^+, and pi cong \tilde{\pi} otimes xi be a cuspidal automorphic representation of GL_n(AA_F) obtained from tilde{pi} by twisting a Hecke character xi. In the case of F^+ = QQ, Michael Harris defined arithmetic automorphic periods for certain tilde{pi} in his Crelle paper 1997, and showed that critical values of automorphic L-functions for pi can be interpreted in terms of these arithmetic automorphic periods. Lin Jie generalized his construction and results to the general totally real field F^+ in her thesis. On the other hand, for certain cuspidal representation Pi of GL_{2n}(F^+), which admits a Shalika model, Grobner and Raghuram related their critical values of L-functions to a non-zero complex number (called Shalika periods). We noticed that the automorphic induction AI(pi) of pi, considered by Harris and Lin, will automatically have a Shalika model, and by comparing common critical values of their identical L-functions, we relate the Shalika periods of AI(pi) with arithmetic automorphic periods of tilde{pi}. In the case F^+=QQ, this comparison will express each arithmetic automorphic period in terms of the corresponding Shalika periods.

Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / Class field theory describes the abelian extensions of a given field K in terms of various class groups of K, and can be viewed as one of the great successes of 20th century number theory. However, the main results in class field theory are pure existence results, and do not give explicit constructions of these abelian extensions. Such explicit constructions are possible for a variety of special cases, such as for the field Q of rational numbers, or for quadratic imaginary fields. When K is a global function field, however, there is a completely explicit description of the abelian extensions of K, utilising the theory of sign-normalised Drinfeld modules of rank one. In this thesis we give detailed survey of explicit class field theory for rational function fields over finite fields, and of the fundamental results needed to master this topic.