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
.
Most widely held works about
R. C Vaughan
 Vaughan, Robert Charles, C.M.G. : Retired Chairman and President, Canadian National Railways( )
 Vaughan, Robert Charles : vicepresident, purchases and stores, Canadian National Rys. and Grand Trunk Ry. System ; also vicepresident in charge of Canadian National Ocean and Lake Services( )
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
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
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
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
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
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
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
1 edition published in 1814 in English and held by 2 WorldCat member libraries worldwide
Mean value theorems for binary Egyptian fractions II by
JingJing Huang(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
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 HardyLittlewood circle method. As a necessary step in the proof, we obtain a nontrivial 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
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 HardyLittlewood circle method. As a necessary step in the proof, we obtain a nontrivial 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
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)
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
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
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
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
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
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
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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
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