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Showing 1 to 16 of 16 for “"quadratic field"”.
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Numerical Tests of Two Conjectures in Fake Real Quadratic Orders
A fake real quadratic order is defined based on an imaginary quadratic field and a prime p but behaves similarly to real quadratic orders. Two conjectures regarding fake real quadratic orders are discussed in the thesis. The first one is the Cohen-Lenstra heuristic. Our computation showed that for …
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A Fundamental Unit of O_K
… the parallel to the classical case and the quadratic field extension that creates the ring O<sub>K</sub>. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute …
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The Structure of the Class Group of Imaginary Quadratic Fields
Let Q(√(-d)) be an imaginary quadratic field with discriminant Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, …
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Lifting Galois Representations in a Conjecture of Figueiredo
… Q and modular forms. Letting M be an imaginary quadratic field, L.M. Figueiredo gave a related conjecture concerning degree 2 irreducible representations of the absolute Galois group of M and their correspondence to homology classes. He experimentally confirmed his conjecture for three …
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Hermitian Maass Lift for General Level
<p>For an imaginary quadratic field $K$ of discriminant $-D$, let $\chi = \chi_K$ be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\chi$ (the hermitian analogue of …
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Topics in analytic number theory
… work on large gaps between primes to imaginary quadratic fields. Suppose K is an imaginary quadratic field, and let N_K denote the field norm on O_K. For x₀ in O_K and r > 0, let (x₀, r) = { x in O_K : |N_K(x − x₀)| < r }. Define G_K(X) = max { r > 0 : there exists x₀ in O_K such that |N_K(x₀)| …
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On the Computation of Invariants in non-Normal, non-Pure Cubic Fields and in Their Normal Closures
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 …
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Elliptic curves with complex multiplication and {u039B}-structures
… reciprocity map associated to an imaginary quadratic field and exhibit, construct a new flat, affine and pro-smooth rigidification of the moduli stack of elliptic curves with complex mulitplication and exibit a relationship between perfect Lambda schemes and periods, both p-adic and analytic.
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Elliptic curves with complex multiplication and {u039B}-structures
… reciprocity map associated to an imaginary quadratic field and exhibit, construct a new flat, affine and pro-smooth rigidification of the moduli stack of elliptic curves with complex mulitplication and exibit a relationship between perfect Lambda schemes and periods, both p-adic and analytic.
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Verification of d-wave pairing symmetry by microwave intermodulation distortion measurements in yttrium barium copper oxide
… of an upturn of the nonlinear coefficient of the quadratic field dependence of the penetration depth. This IMD upturn is limited by the nonlinear Meissner effect that has been predicted for d-wave high-T, superconductors. Various amounts of IMD increase are observed for different films with …
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On Selmer groups and factoring p-adic L-functions
… p-adic L-function associated to an imaginary quadratic field (constructed by Katz) into a product of two Kubota-Leopoldt p-adic L-functions. In 1982, Greenberg proved the corresponding result on the algebraic side involving classical Iwasawa modules, as predicted by the main conjectures for …
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
… be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, and suppose that $E$ has complex multiplication by the ring of integers of $K$. Let us assume the complex $L$-series $L(E/K,s)$ of $E$ over $K$ does not vanish at $s=1$. K. Rubin showed, using Iwasawa …
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Higher Order Couplings in the Clustering of Biased Tracers of Large-Scale Structure
… in the initial conditions. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a powerful framework to model the non-linear clustering due to gravity. In this thesis, we focus on understanding the non-linearities due to galaxy biasing using the EFTofLSS and numerical …
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Základy kvadratických těles
Cílem práce je popsat základy kvadratických těles. Úvodní kapitoly jsou zaměřeny na aritmetiku celých čísel a polynomů. V hlavní části se zabýváme pojmem kvadratického tělesa, celým algebraickým číslům tohoto tělesa, Gaussovu tělesu a Gaussovým celým číslům. Závěr je věnován kvadratickým tělesům, …
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Diskrétně normované řády kvaternionových algeber
Tato práce shrnuje autorův výzkum v oblasti teorie kvaternionových algeber, jejich izomorfismů a maximálních řádů. Nový úhel pohledu na tuto problematiku je umožněn využitím pojmu diskrétní normy. Za hlavní výsledky práce je možná považovat důkaz jednoznačnosti diskrétní normy pro celá čísla, …