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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 169 for “"number theory"”.
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Topics in number theory
The thesis is concerned mainly with topics in the theory of Riemann’s zeta function, but it also includes some contributions to prime number theory and the study of the Möbius function. New conditions are stated for the validity of the quasi-Riemann hypothesis RH (σ₀), that ζ(s) ≠ O for σ > σ₀. The …
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Elements of number theory
… argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empirical core of the dissertation, is the relationship between semantically based noun classification and agreement in …
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L-functions in Number Theory
… has become one of the central objects in Number Theory. The theory of L-functions, which produces a large family of consequences and conjectures in a unified way, concerns their zeros and poles, functional equations, special values and the connections between objects in different fields. …
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Topics in Analytic Number Theory
In the second chapter we study the Multiplicative Partition Function. In the third chapter we study an analog of the abc conjecture for arithmetical functions in r variables over a field K of characteristic zero.
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Topics in Combinatorial Number Theory
In this dissertation we present a number of new results in combinatorial number theory. Chapter I discusses a generalization of B(,2)-sequences which are used in Chapter II and Chapter III to obtain short interval results about k-free values of irreducible polynomials. Chapter IV deals with the …
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Topics in analytic number theory
This thesis, consisting of two chapters, proves several new theorems concerning L-functions and the distribution of primes. In the first chapter, we establish the first explicit form of the Vinogradov–Korobov zero-free region for Dirichlet L-functions. In the second chapter, we generalize recent …
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Topics in analytic number theory
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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Topics in analytic number theory
We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, motivated by work of Iwaniec and Sarnak, we study the question of average …
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Topics in Probability and Number Theory
Made available in DSpace on 2014-12-14T13:09:39Z (GMT). No. of bitstreams: 1 7821224.pdf: 1901482 bytes, checksum: 217b425d68a4aebe0f401f633e9250c7 (MD5) Previous issue date: 1978
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Topics in Multiplicative and Probabilistic Number Theory
A heuristic in analytic number theory stipulates that sets of positive integers cannot simultaneously be additively and multiplicatively structured. The practical verification of this heuristic is the source of a great number of difficult problems, including the well-known Hardy-Littlewood tuples …
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Connecting Number Theory with High School Mathematics
<p>Number theory is the study of natural numbers and one of the oldest branches of mathematics. Elementary number theory concepts are integrated into K-12 learning experience. This paper will identify ideas and methods in elementary number theory that could be connected to K-12 education and taught …
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The local-global principle in number theory
… problems, making Local-Global methods a powerful number theoretic tool. Even when the principle fails, we can sometimes salvage some connection between the local and the global. This thesis aims to give a survey of the basic theory.
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Some Extremal Problems in Additive Number Theory
… defined as the smallest sum of distinct natural numbers whose squares have sum n. Using a modified greedy algorithm, we give a precise asymptotic estimate for t(n) which shows, in particular, that t(n) is very closely approximated by n .
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Problems in number theory and hyperbolic geometry
In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a …
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Combinatorial number theory through diagramming and gesture
Within combinatorial number theory, we study a variety of problems about whole numbers that include enumerative, diagrammatic, or computational elements. We present results motivated by two different areas within combinatorial number theory: the study of partitions and the study of digital …
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Studies on the number theory of orders
… drawn between maximal and nonmaximal orders in a numberfield. Most 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, …
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Sums of Polynomials, Minmax Problems and Number Theory
… minmax problems for fractional parts of real numbers.
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Topics in Analytic, Combinatorial and Probabilistic Number Theory
In the last chapter we consider the problem of determining how large an integer M should be so that almost every subset of {l, ..., N} of size M contains at least one arithmetic progression of length k. We also investigate the length of the longest arithmetic progression in a random subset of …
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