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Showing 1 to 20 of 30 for “"Dedekind"”.
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Analogues of Dedekind Sums
In 1877, R. Dedekind introduced the sum$$s(d, c) = \sum\sbsp{j=1}{c}\left(\left({j\over c}\right)\right)\left(\left({dj\over c}\right)\right),$$which appears in the multiplier system of the Dedekind eta-function as a modular form. A century later, B. C. Berndt did analogous work with the classical …
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Concerning the Dedekind Cut Proposition.
The purpose of this thesis is to prove the Dedekind Cut Proposition using two axioms and a few basic definitions. The Dedekind Cut Proposition states that if H and K are two subsets of the arc AB such that each point of AB belongs to H or K in the order from A to B on AB, then either H has a last …
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Concerning the Dedekind Cut Proposition.
The symbol S will denote the set to which P belongs if and only if P is a point.The statement that the collection G of point sets covers the point set M means that if P is a point of M, then P belongs to some set of the collection G.
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Zeros of the Dedekind Zeta-Function
… of his formula for the nontrivial 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.
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Transformations of Theta-Functions and Analogues of Dedekind Sums
… we refer to as Berndt sums, are analogous to Dedekind sums, which arise in a similar manner from the transformation formula for the logarithm of the Dedekind eta-function. In this thesis, we deduce a number of properties of these sums, and demonstrate the central role they play in a variety of …
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On the spectrum of the metaplectic group with applications to Dedekind sums
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982.
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Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field
… The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into …
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Topological Ramsey Spaces, Associated Ultrafilters, and Their Applications to the Tukey Theory of Ultrafilters and Dedekind Cuts of Nonstandard Arithmetic
… part, we extend results of Blass concerning Dedekind cuts associated to ultrafilter mappings from p-point and weakly-Ramsey ultrafilters to ultrafilter mappings from Ramsey for R1 ultrafilters. Blass associates to each ultrafilter U on a countable set X and each function g with domain X a …
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Moments Of Products Of L-Functions
… distribution of the nontrivial zeros of certain Dedekind zeta-functions. In particular, let K be a quadratic number field. Using the mixed second moments of derivatives of the Dedekind zeta-function attached to K on the critical line, we prove the existence of gaps between consecutive zeros of …
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Various Differents for 0-Dimensional Schemes and Applications
This thesis attempts to investigate the Noether, Dedekind, and Kähler differents for a 0-dimensional scheme X in the projective n-space P^n_K over an arbitrary field K. In particular, we focus on studying the relations between the algebraic structure of these differents and geometric properties of …
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Spectral interpretation of zeros of zeta functions
… are exactly the critical zeros of the Dedekind zeta function of the number field.</p>
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Infinite Series Identities in the Theory of Elliptic Functions and Q-Series
… We extend C. L. Siegel's method of proving the Dedekind-eta function transformation by integrating some selected functions over a positively oriented polygon, generalizing Siegel's integration over a parallelogram. As consequences, we obtain a generalization of the Dedekind-eta function …
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Tensor Products Of Vector Seminormed Spaces
… is a triple consisting of a vector space, a Dedekind complete Riesz space, and a vector valued seminorm, called a vector seminorm, defined on the vector space and taking values in the Riesz space. The collection of vector seminormed spaces with suitably defined morphisms is shown to be a …
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Studies on the number theory of orders
… of the work on orders in this period was done by Dedekind and Kronecker. The twentieth century has witnessed a relative neglect of the nonmaximal orders of a numberfield, which are the algebraic analogues of singular curves, although a few texts, for example the one by Borevich and Shafarevich, do …
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MONOID RINGS AND STRONGLY TWO-GENERATED IDEALS
… property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if …
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L-Fuzzy Relations in Coq
Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and …
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Exhaustivity, continuity, and strong additivity in topological Riesz spaces.
… strong additivity and exhaustive elements of Dedekind s-complete Banach lattices. There is a strong connection between the Diestel-Faires Theorem and the Meyer-Nieberg Lemma in this setting. Also, embedding properties of Banach lattices are linked to the notion of strong additivity. The …
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Fibonacci Sets In Discrepancy Theory and Numerical Integration
… point sets. Furthermore, with the help of Dedekind Sums, we find the L2 discrepancy of rational approximation for the general irrational lattice and characterize the rational lattices for which the L2 discrepancy are optimal. We also introduce quartered Lp discrepancy and prove …
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Hyperconvexity and endpoints in T₀-quasi-metric spaces
… partially ordered set the connection between its Dedekind-MacNeille completion and the q-hyperconvex hull of its natural T₀-quasi-metric space.
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