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Showing 1 to 20 of 349 for “"sums"”.
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Effective estimates for sums of Kloosterman sums, modular forms, and applications
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Analogues of Dedekind Sums
… develops the arithmetic theory of the analogous sums introduced by Berndt. Many properties, both elementary and analytic, are derived. In this thesis we parallel one of the paths laid out by H. Rademacher in his study of $s(d, c).$ New methods are required in the study of $S(d, c).$ As an …
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Sums and covers in categories
… sense of Zurab Janelidze. We study covers and sums at this level, abstracting a number of results and constructions known for coproducts. We examine the dual notion of a product structure and show that these coincide with independence structures of Alex Simpson. We show that morphisms from sum …
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Sign Ambiguities of Gaussian Sums
… and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample …
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Unique Subdirect Sums of Rings
Made available in DSpace on 2014-12-05T21:50:18Z (GMT). No. of bitstreams: 1 6101637.pdf: 2614030 bytes, checksum: c9ba47c0ce33d6adc445b6f4f91df9a3 (MD5) Previous issue date: 1961
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Explicit multiplicative relations between Gauss sums
… that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product …
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Lattice polytopes with distinct pair-sums
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-11-12T15:48:22Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Milos_Curcic.pdf: 1736474 bytes, checksum: 78919c2db9cb41bd6fc66699c7c32e46 (MD5)
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Feynman integrals, hypergeometric functions and nested sums
… in FORM to expand these in terms of nested sums.
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Zeros of partial sums of power series
… unit circle is a limit point of zeros of partial sums of the power series. In this thesis, the relationship between the properties of the function and the behavior of the zeros of its partial sums is investigated. We prove that the set of limit points of xeros of partial sums of rational functions …
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An Asymptotic Expansion for Sums of Random Variables
In this thesis we introduce a local limit theorem for probability
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The density of complex zeros of random sums
… the results he obtained with Shepp to random sums with holomorphic functions that are real-valued on the real line as the basis functions. Our interest in this dissertation is to refine the techniques of random fields pioneered by Rice in his treatment of the questions on real zeros to obtain …
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The Asymptotic Behavior of Birkhoff- and Lacunary Sums
… asymptoic behaviour of Lacunary- and Birkhoff sums. The former are sums formed by periodic functions and exponentially growing sequences of natural numbers. The corresponding summands often exhibit behavior typical of independent and identically distributed random variables. The methods used …
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Sums of Polynomials, Minmax Problems and Number Theory
The study in the second direction is to formulate a new fundamental method to solve some extremal problems. We study certain minmax problems about unit vectors in the plane that are best formulated in terms of complex exponentials. We transform these problems into problems about determining whether …
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Half-integral weight Kloosterman sums and integer partitions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01
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Atiya-Bott theory for orbifolds and Dedkind sums
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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A New Asymptotic Expansion for Sums of Random Variables
… expansions for probability distributions of sums of independent identically distributed random variables. Let X be a random variable with finite variance, and X1, X2, …, a sequence of i.i.d. random variables each with the same distribution as X. In addition, suppose that X has probability …
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