WorldCat Identities

Vaughan, R. C.

Overview
Works: 22 works in 66 publications in 2 languages and 952 library holdings
Genres: Academic theses 
Roles: Author, Other, Thesis advisor
Publication Timeline
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Most widely held works by R. C Vaughan
Multiplicative number theory I : classical theory by Hugh L Montgomery( Book )

3 editions published between 2007 and 2011 in English and held by 30 WorldCat member libraries worldwide

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular, their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. This book comprehensively covers all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. The text is based on courses taught successfully over many years at the University of Michigan, Imperial College, London and Pennsylvania State University
On the fractional parts of x/n and related sequences by B Saffari( Book )

5 editions published in 1976 in English and French and held by 14 WorldCat member libraries worldwide

Theory and applications of numbers without large prime factors( Book )

3 editions published in 1993 in English and held by 9 WorldCat member libraries worldwide

Applications of the Hardy Littlewood method( Book )

2 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide

The year on the Canadian National system by R. C Vaughan( Book )

1 edition published in 1941 in English and held by 2 WorldCat member libraries worldwide

On the representation of numbers as sums of squares, cubes and fourth powers and on the representation of numbers as sums of powers of primes by R. C Vaughan( Book )

2 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide

The elements of Euclid : viz. the first six books, together with the eleventh and twelfth ... also the book of Euclid's Data, in like manner corrected by Euclid( Book )

1 edition published in 1814 in English and held by 2 WorldCat member libraries worldwide

Mean value theorems for binary Egyptian fractions II by Jing-Jing Huang( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

Asymptotic formulae in analytic number theory by Ayla Gafni( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

This dissertation is composed of two main results. The first is an asymptotic formula for $p^k(n)$, the number of partitions of a number $n$ into $k$-th powers. As an immediate consequence of this formula, we derive an asymptotic equivalence for $p^k(n)$ which was claimed without proof in a 1918 paper of Hardy and Ramanujan. The result is established using the Hardy-Littlewood circle method. As a necessary step in the proof, we obtain a non-trivial bound on exponential sums of the form $\sum_{m=1}^q e(\frac{am^k}{q})$. The second result is an asymptotic formula for the number of rational points near planar curves. More precisely, if $f:\mathbb{R}\rightarrow\mathbb{R}$ is a sufficiently smooth function defined on the interval $[\eta,\xi]$, then the number of rational points with denominator no larger than $Q$ that lie within a $\delta$-neighborhood of the graph of $f$ is shown to be asymptotically equivalent to $(\xi-\eta)\delta Q^2$. This result has implications to the field of metric Diophantine approximation
The Life and Times of Grayson County, TX by R. C Vaughan( Book )

1 edition published in 2007 in English and held by 1 WorldCat member library worldwide

THEORY OF NUMBERS( Book )

1 edition published in 1970 in English and held by 1 WorldCat member library worldwide

The collection of papers reports work done under contract on the theory of numbers, particularly to extend sieve methods to reducible polynomials and the distribution of primes in arithmetic progressions to othr sequences. The work in combinatorial mathematics is directed toward combinational designs. Titles of the seven papers are: Mean Values Theorems for a Class of Arithmetic Functions; Sieve Methods - The 'Small' Sieve; Sums of k TH Order Divisor Functions Extended Over the Primes; On the Problem of Erdos, Straus and Schinzel; On the Addition of Sequences of Integers; Thrackles and Deadlock; and, Distances Realized by Sets Covering the Plane. (Author)
Local variation of Euler products by Hugh L Montgomery( )

1 edition published in 2008 in English and held by 1 WorldCat member library worldwide

Higher powers by R. C Vaughan( )

1 edition published in 2000 in English and held by 1 WorldCat member library worldwide

Identification of ochratoxin A producing Aspergillus carbonarius and A. niger clade isolated from grapes using the loop‐mediated isothermal amplification (LAMP) reaction( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Abstract Aims To develop two assays based on the loop‐mediated isothermal amplification (LAMP) of DNA for the quick and specific identification of Aspergillus carbonarius and ochratoxigenic strains of the Aspergillus niger clade isolated from grapes. Methods and Results Two sets of primers were designed based on the polyketide synthase genes involved or putatively involved in ochratoxin A (OTA) biosynthesis in A. carbonarius and A. niger clade. Hydroxynaphthol blue was used as indirect method to indicate DNA amplification. The limit of detection of both assays was comparable to that of a PCR reaction. Specificities of the reactions were tested using DNA from different black aspergilli isolated from grapes. The two LAMP assays were then used to identify A. carbonarius and ochratoxigenic A. niger and A. awamori grown in pure cultures without a prior DNA extraction. Conclusions The two LAMP assays permitted to quickly and specifically identify DNA from OTA‐producing black aspergilli, as well as isolates grown in pure culture. Significance and Impact of the Study Monitoring vineyards for the presence of OTA‐producing strains is part of the measures to minimize the occurrence of OTA in grape products. The two LAMP assays developed here could be potentially used to speed the screening process of vineyards for the presence of OTA‐producing black aspergilli
On the estimation of trigonometrical sums over primes, and related questions by R. C Vaughan( Book )

1 edition published in 1977 in English and held by 1 WorldCat member library worldwide

A special case of Vinogradov's mean value theorem by R. C Vaughan( )

1 edition published in 1997 in English and held by 1 WorldCat member library worldwide

 
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Multiplicative number theory I : classical theory
Alternative Names
Bob Vaughan matemático británico

Robert Charles Vaughan britischer Mathematiker

Robert Charles Vaughan Brits wiskundige

Robert Charles Vaughan mathématicien britannique

Vaughan, R. C.

Vaughan, Robert C.

Vaughan Robert C. 1945-....

Von, R.

Воган, Боб британский математик

ボブ・ヴォーン

罗伯特·查尔斯·沃恩

Languages
English (27)

French (1)

Covers
The Life and Times of Grayson County, TX