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Showing 1 to 20 of 38 for “"number field"”.

  1. An Introduction to the General Number Field Sieve

    Briggs, Matthew EdwardVirginia Tech1998

    … the RSA system would be nullified. The General Number Field Sieve algorithm is the fastest known method for factoring large integers. Research and development of this algorithm within the past five years has facilitated factorizations of integers that were once speculated to require thousands of …

    vt Repository record

  2. On the Galois module structure of the units and ray classes of a real abelian number field

    All, Timothy JamesThe Ohio State University2013

    … group and the group of units of a real abelian number field. Specifically, we derive explicit annihilators of the ideal ray class groups in the vein of the classical Stickelberger theorems. This is made possible by generalizing a theorem of Rubin which in turn allows us to describe a …

    ohiolink Repository record

  3. Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field

    Rezola, Nolberto2015

    … of algebraic integers of an imaginary quadratic number field.</p>

    csusb Repository record

  4. The Divisibility and Modular Properties of Kth-Order Linear Recurrences Over The Ring of Integers of an Algebraic Number Field With Respect to Prime Ideals

    Somer, Lawrence EricUniversity of Illinois at Urbana-Champaign2014

    Let K be an algebraic number field and R its ring of integers. Let k (GREATERTHEQ) 2 and let (w) be a kth-order linear recurrence over R satisfying the recursion relation (1) w(,n+k) = a(,1)w(,n+k-1) + a(,2)w(,n+k-2) +...+ a(,k)w(,n). Those recurrences (u) satisfying (1) for which u(,0) = u(,1) …

    uiuc Repository record

  5. Spectral interpretation of zeros of zeta functions

    Waldhauser, Tamas

    <p>For every algebraic number field we construct an operator on a separable Hilbert space, whose eigenvalues are exactly the critical zeros of the Dedekind zeta function of the number field.</p>

    unh-thes Repository record

  6. PSL(2,7)-Extensions with Certain Ramification at Two Primes

    Simpson, Glen E.2004

    … Hunter search in order to find a degree 7 number field K ramified at primes q and p with discriminant d(K)=q^6 p^2 where q=11 and 2<p<104. The number field we seek will satisfy certain criteria allowing for refinement of a conjecture of Ash, Doud, and Pollack. In the course of our search we …

    byu Repository record

  7. Trinomials Defining Quintic Number Fields

    Patsolic, Jesse LeighWake Forest University2014

    Given a number field $K$, how does one find polynomials $f(x)$,

    wfu Repository record

  8. The Least Prime Number That Splits Completely In S3-Sextic Number Fields

    Ge, Zhenchao2019

    <p>In number theory, an integer n is quadratic residue modulo an odd prime p if n is congruent to a perfect square modulo p. Otherwise, n is is called a quadratic nonresidue. Bounding the least prime quadratic residue and the least quadratic nonresidue are two very classical problems in number …

    mississippi Repository record

  9. Relative oriented class groups of quadratic extensions

    O'Connor, Kelly A., author, Pries, Rachel, advisor, Achter, Jeffrey, committee member, Shoemaker, Mark, committee member, Rugenstein, Maria, committee memberColorado State University. Libraries2024

    … 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 classes of quadratic orders and classes of …

    colostate Repository record

  10. Computing the Cassels-Tate Pairing for Jacobian Varieties of Genus Two Curves

    Yan, JialiUniversity of Cambridge2021

    … variety of a genus two curve defined over a number field K. The main focus of this thesis is on computing the Cassels-Tate pairing on the 2-Selmer group of J. We start by studying the Cassels-Tate pairing when J admits a Richelot 􏰑 isogeny φ : J → J. Suppose all points in J[2] are defined …

    cambridge Repository record

  11. Massey products in the Galois cohomology of number fields

    Vogel, DenisUniversität Heidelberg

    … of Q and of the Galois group of the p-class field tower of a quadratic number field. This relation structure is described in terms of Massey products in the Galois cohomology of number fields. A connection is given to Milnor invariants and Redei symbols. In particluar, we prove a number …

    heid-diss Repository record

  12. Zeros of the Dedekind Zeta-Function

    Alsharif, Mashael2020

    … zeros of the Dedekind zeta-function of a Galois number field, and use this formula and Fourier analysis to prove an estimate for the proportion of distinct zeros, assuming the Generalized Riemann Hypothesis.

    mississippi Repository record

  13. p-adic L-functions of automorphic forms

    Deppe, HolgerUniversität Bielefeld

    Let F be a number field, p a prime number. To an (adelic) automorphic representation of GL2 over F (with certain conditions at places above p and ∞) we construct a p-adic L-function which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization …

    bielefeld Repository record

  14. Problems involving relative integral bases for quartic number fields

    Hymo, John A.Virginia Tech1990

    … of whether or not a relative extension of number fields has a relative integral basis is considered. In Chapters 2 and 3 we use a criteria of Mann to determine when a cyclic quartic field or a pure quartic field has an integral basis over its quadratic subfield. In the final chapter we …

    vt Repository record

  15. ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|

    Chen, CangxiongUniversity of Cambridge2015

    … 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 …

    cambridge Repository record

  16. Towards a topological proof of Wright's Theorem

    de Langis, Mathieu2024

    … concerns the asymptotic behavior of the number of degree-n extensions of a number field with Galois group permutation-isomorphic to G. Using the function field analogy, a similar conjecture can be made for finite extensions of F_q(t), where q is a power of a prime. In fact, a similar …

    umn Repository record

  17. Algorithmic Aspects of Biquadratic, Cubic and Radical Function Fields

    Wu, QingquanUniversity of Illinois at Urbana-Champaign2015

    … integral basis of a cyclic biquadratic function field are simple, explicit and efficient. The computation of the unit group on a global bicyclic biquadratic function field generalizes and simplifies Kubota's work [Kub56) to function fields. It thus settles this question for all global bicyclic …

    uiuc Repository record

  18. Improving regulator verification and compact representations in real quadratic fields

    Silvester, AlanGraduate Studies2013

    … verifies the regulator of a real quadratic number field and refinements to the concept of a compact representation of a quadratic integer, originally given by Buchmann, Thiel, and Williams [12]. In addition, we consider the well-known applications of this theory to principal ideal testing, …

    calgary Repository record

  19. On the Computation of Invariants in non-Normal, non-Pure Cubic Fields and in Their Normal Closures

    Cline, Danny O.Virginia Tech2004

    Let K=Q(theta) be the algebraic number field formed by adjoining theta to the rationals where theta is a real root of an irreducible monic cubic polynomial f(x) in Z[x]. If theta is not the cube root of a rational integer, we call the field K a non-pure cubic field, and if K doesn't contain the …

    vt Repository record

  20. F-virtual Abelian Varieties and Rallis Inner Product Formula

    Wu, Chenyan2011

    … Abelian varieties of GL2-type where F is a number field. We show the relation between these Abelian varieties and those defined over F. We compare their l-adic representations and study the modularity of F-virtual Abelian varieties of GL2-type. Then we construct their moduli spaces and in …

    columbia-diss Repository record

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