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Showing 1 to 15 of 15 for “"Class Number"”.
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Infrastructure, Arithmetic, and Class Number Computations in Purely Cubic Function Fields of Characteristic at Least 5
… we describe methods to compute the divisor class number, h, of K, and in the case that O has unit rank 1 or 2, the regulator and ideal class number of O as well. A method of Scheidler and Stein [SS07, SS08] determines sharper upper and lower bounds on h, for a given cubic function field, …
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Quintic Abelian Fields
… finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class …
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ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|
… to Eisenstein series of level one defined for a number field with class number one and obtained a function analogous to the logarithm of the absolute value of the eta function. In this thesis we reformulate Asai’s function adelically using the theory of admissible representations for GL2 and …
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Units and class groups of imaginary octic fields
In this dissertation class groups and unit groups of number fields with elementary Galois groups of order 4 and 8 are considered. In chapter 3 we consider bicyclic biquadratic extensions K/k and give a method for determining the structure of the 2-class group of K. In chapters 4 and 5 this method …
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Irreducible elements in algebraic number fields
… involving irreducible elements in algebraic number fields. The first question is: Given an algebraic integer β in a field with class number greater than two, how many different lengths of factorizations into irreducibles exist? The distribution into ideal classes of the prime ideals whose …
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Numerical Tests of Two Conjectures in Fake Real Quadratic Orders
… quadratic orders for which the odd part of the class number is one converges to C=0.754458..., which equals exactly the proportion of real quadratic fields for which the odd part of the class number is one. The second one is the Ankeny-Artin-Chowla conjecture, which states that D∤b where b is …
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The Structure of the 2-Sylow Subgroups of the Ideal Class Groups of Imaginary Bicyclic Biquadratic Fields
In this dissertation class groups of imaginary bicyclic biquadratic fields are considered. In chapter 1 we develop a method for determining the structure of the 2-class group of K. In chapters 3, 4, and 5 this method is applied to determine all imaginary bicyclic biquadratic extensions of Q with …
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Genus Fields and Central Extensions of Number Fields
… (narrow) genus group of an abelian extension of number fields using a four term exact sequence of abelian groups derived from work of Frohlich. There are two main results. First, if L/K is a cyclic l-extension, where l is a prime not dividing h(,K)('+), the narrow class number of K, then we …
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On the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closures
… free rational integer <i>m</i> to the rational numbers we construct a cubic field. If we adjoin the cube roots of distinct cube free rational integers <i>m</i> and <i>n</i> to the rational numbers we construct a bicubic field. The number theoretic invariants for the cubic fields and their normal …
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Elementary music educators' adaptive teaching strategies for integrated students with disabilities
… when adaptations relating to socialization, classroom management, physical environment, activities, musical understandings, or required cognitive skills are implemented; and the extent that training, teaching experience, number of students with disabilities integrated into a single music …
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Relative oriented class groups of quadratic extensions
In 2018 Zemková defined relative oriented class groups associated to quadratic extensions of number fields L/K, extending work of Bhargava concerning composition laws for binary quadratic forms over number fields of higher degree. This work generalized the classical correspondence between ideal …
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Improved Arithmetic in the Ideal Class Group of Imaginary Quadratic Number Fields with an Application to Integer Factoring
… to arithmetic and exponentiation in the ideal class group of imaginary quadratic number fields for the Intel x64 architecture. This is useful in tabulating the class number and class group structure, but also as an application to a novel integer factoring algorithm called “SuperSPAR”. SuperSPAR …
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An Evaluation of Structured Navigation for Subject Searching in Online Catalogues
… through 1988 in the English language in the LC classes HB-HJ (Economics, Business, etc.). For each record, the verbal description of the assigned LC class number found in the printed schedules was added as a subject descriptor to augment the subject cataloging provided by the Library of …
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Explicit moduli spaces for curves of genus 1 and 2
… and place them within the Enriques--Kodaira classification in many cases. As a corollary we deduce that the Humbert surface of discriminant $N^2$ is rational if and only if $N \leq 16$, or if $N = 18$, $20$, or $24$. We then study $N$-congruences between quadratic twists of elliptic curves. …