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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 35 for “"Prime number"”.
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Prime and Quasi-Prime Number Races
"We review the body of work done on prime number races, specifically the results involving infinitely many lead changes in prime number races. We describe a computational way of showing that any race has infinitely many lead changes and greatly expand the known results in this area. An extension of …
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The prime number theorem: Analytic and elementary proofs
Three proofs of the prime number theorem are presented. The �rst is a heavily analytic proof based on early accounts. Cauchy's residue theorem and various results relating to the Riemann zeta function play a vital role. A weaker result than the prime number theorem is used for the proof, namely …
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Prime Number-Based Hierarchical Data Labeling Scheme for Relational Databases
… relationships between nodes. There exist a number of different ways to capture and manage hierarchical data while preserving such relationships. For instance, one may use a custom system designed for a specific kind of hierarchy. Object oriented databases may also be used to model …
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A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions
… that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of …
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The Least Prime Number That Splits Completely In S3-Sextic Number Fields
<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 …
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Historic development of prime numbers
… of this thesis is to investigate the history of prime numbers and development of prime number theory. There are three major sections to this thesis, Ancient times, Dark Ages, and Modern times. The ancient time's section has topics on the `Ishango Bone', `Rhine Papyrus' with an investigation of …
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Systematic Composition and Intuition in a Concerto for Organ and Orchestra
… of decimals that are created from certain prime-number denominators, and focuses on the prime number 17. Shows how these decimals can be transformed by converting them to different number bases. Looks at the Golden Proportion and its use in creating formal structures. Examines compositional …
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On the Theory of Zeta-functions and L-functions
… formulations and approaches to the proof of the Prime Number Theorem and the Riemann Hypothesis. These two topics constitute the main theme of this thesis. For the Prime Number Theorem, we provide a thorough discussion that compares and contrasts Norbert Wiener's proof with that of Newman's short …
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Algorithmic approaches to graph states under the action of local Clifford groups
… space ... (q being a power of some prime number) which can be described by graphs with edges labeled from the field of order q, Fq. Graph states are determined as a common eigenvector of independent elements of the n-fold Pauli group, on which the local Clifford group has a natural …
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Explicit Estimates for Functions of Primes in Arithmetic Progressions
… numerical estimates for the error term in the prime number theorem for arithmetic progressions, and Waring's problem for cubes.
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On the Projective Characters of the Finite Chevalley Groups
Let p be a prime number, let m be a positive integer and let G be a universal Chevalley group constructed over a field of order ${\rm p\sp{m}}.$ We consider the modular representations (in characteristic p) of the group G. More precisely, we study the Brauer characters of G, concentrating on the …
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p-adic L-functions of automorphic forms
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 …
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Display structures on de Rham-Witt cohomology
Let $p$ be a prime number and $R$ be a noetherian and $F$-finite ring where $p \in R$ is nilpotent. In this thesis we prove that the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a display structure $\underline{P}^l$ if the crystalline cohomology $H^l_{crys}(X,W(R))$ is …
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Efficient algorithm to construct phi function in vector space secret sharing scheme and application of secret sharing scheme in Visual Cryptography
… vector space <em>Zdp</em>, where <em>p</em> is a prime number and <em>d</em> is a positive number. There is no known algorithm to construct such a function in general. We developed an efficient algorithm to construct function for some special secret sharing scheme. We also give an algorithm to …
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
… one of the most important open problems in number theory today. Let $E$ 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 …
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Realising The Smooth Representations Of GL2(O_F) Using p-adic Geometric Methods
Let p be an odd prime number and F be a finite extension of the p-adic numbers Q_p with valuation ring O_F and residue field k. In this thesis, we study the smooth representation theory of the profinite group GL_2(OO_F) using the theory of dagger analytic geometry developed by Grosse-Kl\"onne …
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On Beurling's Theory of Generalized Numbers
… 255-291), we consider a set of generalized prime numbers $P=\{1<p\sb1\le p\sb2\le\...\}$ and the set of generalized integers $N=\{n\sb1=1\le n\sb2\le\...\}$ generated by P. We let $N(x)$ be the counting function of the set N. In this thesis we give continuous versions of generalized number …
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Selmer groups as flat cohomology groups
Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined by the mod pm Galois representation A[pm]; we show, however, that this is the …
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Double-interval technique for higher order harmonic generation of a quantum dot mode-locked laser
… technique utilizes the stimulation of the prime number harmonics in unison in order to achieve higher order harmonics. The laser in this study has a fundamental frequency of approximately 6.0 GHz and its second, third, fifth, sixth, and tenth harmonics are presented.'
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