Robert Charles Vaughan

    • 1519 Citations
    • 20 h-Index
    1970 …2018
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    Research Output 1970 2018

    • 1519 Citations
    • 20 h-Index
    • 78 Article
    • 1 Chapter
    • 1 Comment/debate
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    Article
    2018

    Corrigendum to “On the number of partitions into primes”

    Vaughan, R. C., May 1 2018, In : Ramanujan Journal. 46, 1, p. 307-308 2 p.

    Research output: Contribution to journalArticle

    Partition

    The asymptotic formula in Waring's problem: Higher order expansions

    Vaughan, R. C. & Wooley, T. D., Sep 1 2018, In : Journal fur die Reine und Angewandte Mathematik. 2018, 742, p. 17-46 30 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Natural number
    Asymptotic Formula
    Asymptotic Expansion
    Higher Order
    1 Citation (Scopus)

    The divisor function on residue classes II

    Pongsriiam, P. & Vaughan, R. C., Jan 1 2018, In : Acta Arithmetica. 182, 2, p. 133-181 49 p.

    Research output: Contribution to journalArticle

    Divisor Function
    Arithmetic sequence
    Class
    2017

    Diophantine Approximation on Manifolds and Lower Bounds for Hausdorff Dimension

    Beresnevich, V., Lee, L., Vaughan, R. C. & Velani, S., Jan 1 2017, In : Mathematika. 63, 3, p. 762-779 18 p.

    Research output: Contribution to journalArticle

    Diophantine Approximation
    Hausdorff Measure
    Hausdorff Dimension
    Submanifolds
    Lower bound
    4 Citations (Scopus)

    Diophantine approximation on manifolds and the distribution of rational points: Contributions to the convergence theory

    Beresnevich, V., Vaughan, R. C., Velani, S. & Zorin, E., May 1 2017, In : International Mathematics Research Notices. 2017, 10, p. 2885-2908 24 p.

    Research output: Contribution to journalArticle

    Diophantine Approximation
    Convergence Theory
    Rational Points
    Nondegeneracy
    Strictly
    Binary Quadratic Forms
    Legendre
    Discriminant
    Integer
    Quadratic form
    2015
    7 Citations (Scopus)

    Squares: Additive questions and partitions

    Vaughan, R. C., Aug 5 2015, In : International Journal of Number Theory. 11, 5, p. 1367-1409 43 p.

    Research output: Contribution to journalArticle

    Partition
    Exceptional Sets
    Ternary
    Asymptotic Formula
    7 Citations (Scopus)

    The divisor function on residue classes I

    Pongsriiam, P. & Vaughan, R. C., Jan 1 2015, In : Acta Arithmetica. 168, 4, p. 369-381 13 p.

    Research output: Contribution to journalArticle

    Divisor Function
    Arithmetic sequence
    Class
    2 Citations (Scopus)

    Zeros of Dirichlet series

    Vaughan, R. C., Dec 2015, In : Indagationes Mathematicae. 26, 5, p. 897-909 13 p.

    Research output: Contribution to journalArticle

    Dirichlet Series
    Riemann hypothesis
    Zero
    Riemann zeta function
    Argand diagram
    2014

    Integer points on elliptic curves

    Vaughan, R. C., Jan 1 2014, In : Rocky Mountain Journal of Mathematics. 44, 4, p. 1377-1382 6 p.

    Research output: Contribution to journalArticle

    Integer Points
    Elliptic Curves
    Integral Solution
    3 Citations (Scopus)

    The general Goldbach problem with Beatty primes

    Vaughan, R. C., Aug 2014, In : Ramanujan Journal. 34, 3, p. 347-359 13 p.

    Research output: Contribution to journalArticle

    Hardy-Littlewood Method
    Finite Type
    Prime number
    Integer
    Form
    2 Citations (Scopus)

    Waring's problem for Beatty sequences and a local to global principle

    Banks, W. D., Güloǧlu, A. M. & Vaughan, R. C., 2014, In : Journal de Theorie des Nombres de Bordeaux. 26, 1, p. 1-16 16 p.

    Research output: Contribution to journalArticle

    Additive number Theory
    Waring's problem
    Natural number
    Theorem
    Form
    2013
    1 Citation (Scopus)

    On the exceptional set for binary Egyptian fractions

    Huang, J. J. & Vaughan, R. C., Aug 2013, In : Bulletin of the London Mathematical Society. 45, 4, p. 861-874 14 p.

    Research output: Contribution to journalArticle

    Exceptional Sets
    Binary
    Integer
    Diophantine equation
    Asymptotic Formula
    2012
    1 Citation (Scopus)

    Mean value theorems for binary Egyptian fractions II

    Huang, J. J. & Vaughan, R. C., Nov 1 2012, In : Acta Arithmetica. 155, 3, p. 287-296 10 p.

    Research output: Contribution to journalArticle

    Dirichlet L-function
    Mean value theorem
    Gaussian distribution
    Binary
    2011
    12 Citations (Scopus)

    Inhomogeneous Diophantine approximation on planar curves

    Beresnevich, V. V., Vaughan, R. C. & Velani, S. L., Apr 1 2011, In : Mathematische Annalen. 349, 4, p. 929-942 14 p.

    Research output: Contribution to journalArticle

    Planar Curves
    Diophantine Approximation
    Simultaneous Approximation
    Rational Points
    Metric
    5 Citations (Scopus)

    Mean value theorems for binary Egyptian fractions

    Huang, J. & Vaughan, R. C., Sep 1 2011, In : Journal of Number Theory. 131, 9, p. 1641-1656 16 p.

    Research output: Contribution to journalArticle

    Mean value theorem
    Vary
    Binary
    Diophantine equation
    Number of Solutions
    2008

    Local variation of euler products

    Montgomery, H. L. & Vaughan, R. C., Jan 1 2008, In : Functiones et Approximatio, Commentarii Mathematici. 39, 2, p. 273-288 16 p.

    Research output: Contribution to journalArticle

    Euler Product
    Multiplicative Functions
    Dirichlet Series
    Mean Value
    9 Citations (Scopus)

    On the number of partitions into primes

    Vaughan, R. C., Jan 1 2008, In : Ramanujan Journal. 15, 1, p. 109-121 13 p.

    Research output: Contribution to journalArticle

    Logarithmic integral
    Partition
    Distribution of Primes
    Elementary Functions
    Asymptotic Formula
    2006
    44 Citations (Scopus)

    Diophantine approximation on planar curves: The convergence theory

    Vaughan, R. C. & Velani, S., Oct 1 2006, In : Inventiones Mathematicae. 166, 1, p. 103-124 22 p.

    Research output: Contribution to journalArticle

    Planar Curves
    Diophantine Approximation
    Convergence Theory
    Divergence
    Complement
    2005
    4 Citations (Scopus)

    A variance for k-free numbers in arithmetic progressions

    Vaughan, R. C., Jan 1 2005, In : Proceedings of the London Mathematical Society. 91, 3, p. 573-597 25 p.

    Research output: Contribution to journalArticle

    Arithmetic sequence
    2003

    A mean value theorem for cubic fields

    Vaughan, R. C., May 1 2003, In : Journal of Number Theory. 100, 1, p. 169-183 15 p.

    Research output: Contribution to journalArticle

    Dedekind zeta Function
    Abscissa
    Cubic Fields
    Mean value theorem
    Denote
    2 Citations (Scopus)

    Moments for primes in arithmetic progressions, I

    Vaughan, R. C., Nov 1 2003, In : Duke Mathematical Journal. 120, 2, p. 371-383 13 p.

    Research output: Contribution to journalArticle

    Arithmetic sequence
    Moment
    Approximation
    1 Citation (Scopus)

    Moments for primes in arithmetic progressions, II

    Vaughan, R. C., Nov 1 2003, In : Duke Mathematical Journal. 120, 2, p. 385-403 19 p.

    Research output: Contribution to journalArticle

    Arithmetic sequence
    Moment
    Approximation
    2001

    A generalised divisor problem in memorium Hans-Egon Richert

    Vaughan, R. C., Aug 20 2001, In : Journal fur die Reine und Angewandte Mathematik. 2001, 537, p. 151-163 13 p.

    Research output: Contribution to journalArticle

    Divisor
    15 Citations (Scopus)
    Distribution of Primes
    Arithmetic sequence
    1 Citation (Scopus)

    On sigma-PHI numbers

    Vaughan, R. C. & Weis, K. L., Jan 1 2001, In : Mathematika. 48, 1-2, p. 169-189 21 p.

    Research output: Contribution to journalArticle

    2000
    22 Citations (Scopus)

    Further improvements in Waring's problem, IV: Higher powers

    Vaughan, R. C. & Wooley, T. D., Dec 1 2000, In : Acta Arithmetica. 94, 3, p. 203-285 83 p.

    Research output: Contribution to journalArticle

    Waring's problem
    High Power
    1998
    2 Citations (Scopus)

    Hardy's legacy to number theory

    Vaughan, R. C., Oct 1 1998, In : Journal of the Australian Mathematical Society. 65, 2, p. 238-266 29 p.

    Research output: Contribution to journalArticle

    Number theory
    9 Citations (Scopus)
    Arithmetic sequence
    Asymptotic Formula
    progressions
    Modulus
    Class
    6 Citations (Scopus)
    Arithmetic sequence
    Asymptotic Formula
    progressions
    Asymptotic distribution
    Modulus
    6 Citations (Scopus)

    On the distribution of generating functions

    Vaughan, R. C. & Wooley, T. D., Mar 1998, In : Bulletin of the London Mathematical Society. 30, 2, p. 113-122 10 p.

    Research output: Contribution to journalArticle

    Generating Function
    16 Citations (Scopus)

    On the exponential sum over k-free numbers

    Brüdern, J., Granville, A., Perelli, A., Vaughan, R. C. & Wooley, T. D., Mar 15 1998, In : Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 356, 1738, p. 739-761 23 p.

    Research output: Contribution to journalArticle

    Exponential Sums
    Generating Function
    Minor arc
    Circle Method
    Dissection
    1997
    11 Citations (Scopus)

    A special case of Vinogradov's mean value theorem

    Vaughan, R. C. & Wooley, T. D., Jan 1 1997, In : Acta Arithmetica. 79, 3, p. 193-204 12 p.

    Research output: Contribution to journalArticle

    Mean value theorem
    1996
    10 Citations (Scopus)

    On the eigenvalues of Redheffer's matrix, II

    Vaughan, R. C., Apr 1 1996, In : Journal of the Australian Mathematical Society. 60, 2, p. 260-273 14 p.

    Research output: Contribution to journalArticle

    Radius
    Eigenvalue
    Estimate
    1995
    37 Citations (Scopus)

    Further improvements in Waring's problem

    Vaughan, R. C. & Wooley, T. D., Sep 1 1995, In : Acta Mathematica. 174, 2, p. 147-240 94 p.

    Research output: Contribution to journalArticle

    Waring's problem
    23 Citations (Scopus)

    On a certain nonary cubic form and related equations

    Vaughan, R. C. & Wooley, T. D., Jan 1 1995, In : Duke Mathematical Journal. 80, 3, p. 669-735 67 p.

    Research output: Contribution to journalArticle

    Form
    23 Citations (Scopus)

    Some Remarks on Gauss Sums Associated with Kth Powers

    Montgomery, H. L., Vaughan, R. C. & Wooley, T. D., Jan 1 1995, In : Mathematical Proceedings of the Cambridge Philosophical Society. 118, 1, p. 21-33 13 p.

    Research output: Contribution to journalArticle

    Gauss Sums
    1994
    11 Citations (Scopus)

    Further improvements in waring’s problem, II: Sixth powers

    Vaughan, R. C. & Wooley, T. D., Jan 1 1994, In : Duke Mathematical Journal. 76, 3, p. 683-710 28 p.

    Research output: Contribution to journalArticle

    1991
    1 Citation (Scopus)

    On a problem related to one of littlewood and offord

    Vaughan, R. C. & Wooley, T. D., Jan 1 1991, In : Quarterly Journal of Mathematics. 42, 1, p. 379-386 8 p.

    Research output: Contribution to journalArticle

    25 Citations (Scopus)

    On waring’s problem: Some refinements

    Vaughan, R. C. & Wooley, T. D., Jan 1 1991, In : Proceedings of the London Mathematical Society. s3-63, 1, p. 35-68 34 p.

    Research output: Contribution to journalArticle

    Refinement
    1990
    26 Citations (Scopus)

    The k-dimensional Duffin and Schaeffer conjecture

    Pollington, A. D. & Vaughan, R. C., Dec 1990, In : Mathematika. 37, 2, p. 190-200 11 p.

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Theorem with Applications in Coding and Matching Problems

    Nandi, A. K. & Vaughan, R. C., Jan 1 1990, In : Electronics Letters. 26, 23, p. 1928-1930 3 p.

    Research output: Contribution to journalArticle

    Vector quantization
    Costs
    1989
    115 Citations (Scopus)

    A new iterative method in Waring's problem

    Vaughan, R. C., Jul 1 1989, In : Acta Mathematica. 162, 1, p. 1-71 71 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Iteration
    20 Citations (Scopus)

    A New Iterative Method In Waring's Problem II

    Vaughan, R. C., Jan 1 1989, In : Journal of the London Mathematical Society. s2-39, 2, p. 219-230 12 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Iteration
    26 Citations (Scopus)

    On Waring's Problem For Cubes II

    Vaughan, R. C., Apr 1989, In : Journal of the London Mathematical Society. s2-39, 2, p. 205-218 14 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Regular hexahedron
    1988
    9 Citations (Scopus)

    The l1mean of exponential sums over primes

    Vaughan, R. C., Mar 1988, In : Bulletin of the London Mathematical Society. 20, 2, p. 121-123 3 p.

    Research output: Contribution to journalArticle

    Exponential Sums
    1987

    Adventures in arithmetick, or: How to make good use of a fourier transform

    Vaughan, R. C., Jun 1 1987, In : The Mathematical Intelligencer. 9, 2, p. 53-60 8 p.

    Research output: Contribution to journalArticle

    Fourier transform
    1986
    10 Citations (Scopus)

    On waring's problem: One square and five cubes

    Vaughan, R. C., Mar 1 1986, In : Quarterly Journal of Mathematics. 37, 1, p. 117-127 11 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Regular hexahedron
    99 Citations (Scopus)

    On Waring's problem for cubes

    Vaughan, R. C., Jan 1 1986, In : Journal fur die Reine und Angewandte Mathematik. 1986, 365, p. 122-170 49 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Regular hexahedron
    40 Citations (Scopus)

    On Waring'S Problem For Smaller Exponents. Ii

    Vaughan, R. C., Jun 1986, In : Mathematika. 33, 1, p. 6-22 17 p.

    Research output: Contribution to journalArticle

    Exponent