Robert Charles Vaughan

Research output

Research output per year 1970 1973 1974 1977 1986 1989 1995 1998 2001 2003 2014 2015 2017 2018 2021 2022

• 84 Article
• 1 Chapter
• 1 Comment/debate
• 1 Review article

Research output per year

Research output per year

Search results

• 2022

  Sums of two unlike powers in arithmetic progressions

  Brüdern, J. & Vaughan, R. C., Jul 2022, In: European Journal of Mathematics. 8, p. 182-213 32 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Arithmetic sequence 100%
• 2021

  A Montgomery–Hooley Theorem for sums of two cubes

  Brüdern, J. & Vaughan, R. C., Dec 2021, In: European Journal of Mathematics. 7, 4, p. 1616-1644 29 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Arithmetic sequence 100%
  • Regular hexahedron 85%
  • Integer 47%
  • Theorem 36%
  2 Scopus citations

• Diophantine approximation on curves and the distribution of rational points: Contributions to the divergence theory

  Beresnevich, V., Vaughan, R. C., Velani, S. & Zorin, E., Sep 17 2021, In: Advances in Mathematics. 388, 107861.

  Research output: Contribution to journal › Article › peer-review

  • Diophantine Approximation 100%
  • Rational Points 90%
  • Divergence 73%
  • Curve 50%
  • Explicit Methods 30%
  2 Scopus citations

• On generating functions in additive number theory, II: lower-order terms and applications to PDEs

  Brandes, J., Parsell, S. T., Poulias, C., Shakan, G. & Vaughan, R. C., Feb 2021, In: Mathematische Annalen. 379, 1-2, p. 347-376 30 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Additive number Theory 100%
  • Fractal Dimension 70%
  • Generating Function 57%
  • Term 36%
  • Form 27%
  5 Scopus citations

• The divisor function on residue classes III

  Pongsriiam, P. & Vaughan, R. C., Nov 2021, In: Ramanujan Journal. 56, 2, p. 697-719 23 p.

  Research output: Contribution to journal › Article › peer-review

  • Divisor Function 100%
  • Moment 52%
  • Expected Value 25%
  • Error term 25%
  • Asymptotic Formula 23%
  1 Scopus citations
• 2020

  Density of positive diagonal binary quadratic forms

  Hanson, B. & Vaughan, R., 2020, In: Acta Arithmetica. 193, 1, p. 1-48 48 p.

  Research output: Contribution to journal › Review article › peer-review
  1 Scopus citations

• On Some Questions of Partitio Numerorum: Tres Cubi

  Vaughan, R. C., Jan 1 2020, (Accepted/In press) In: Glasgow Mathematical Journal.

  Research output: Contribution to journal › Article › peer-review

  • Regular hexahedron 100%
• 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 journal › Article › peer-review

• 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 journal › Article › peer-review

  • Waring's problem 100%
  • Asymptotic Formula 62%
  • Natural number 62%
  • Asymptotic Expansion 57%
  • Higher Order 47%
  2 Scopus citations

• The divisor function on residue classes II

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

  Research output: Contribution to journal › Article › peer-review
  10 Scopus citations
• 2017

  Diophantine Approximation on Manifolds and Lower Bounds for Hausdorff Dimension

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

  Research output: Contribution to journal › Article › peer-review

  • Diophantine Approximation 100%
  • Hausdorff Measure 95%
  • Hausdorff Dimension 81%
  • Submanifolds 75%
  • Lower bound 54%
  7 Scopus citations

• 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 journal › Article › peer-review

  Open Access

  • Diophantine Approximation 100%
  • Convergence Theory 98%
  • Rational Points 90%
  • Nondegeneracy 30%
  • Strictly 21%
  20 Scopus citations

• The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant

  Hanson, B., Vaughan, R. C. & Zhang, R., Oct 2017, In: Journal of Number Theory. 179, p. 3-16 14 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Binary Quadratic Forms 100%
  • Legendre 75%
  • Discriminant 75%
  • Integer 38%
  • Quadratic form 34%
• 2016

  Goldbach’s conjectures: A historical perspective

  Vaughan, R. C., Jan 1 2016, Open Problems in Mathematics. Springer International Publishing, p. 479-520 42 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter

  • Goldbach's conjecture 100%
  • Historical Perspective 70%
  • Influence 24%
  • Binary 24%
  • Range of data 19%
  2 Scopus citations
• 2015

  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 journal › Article › peer-review

  • Partition 100%
  • Exceptional Sets 57%
  • Ternary 45%
  • Asymptotic Formula 42%
  15 Scopus citations

• 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 journal › Article › peer-review
  19 Scopus citations

• Zeros of Dirichlet series

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

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Dirichlet Series 100%
  • Riemann hypothesis 49%
  • Zero 43%
  • False 42%
  • Riemann zeta function 40%
  3 Scopus citations
• 2014

  Integer points on elliptic curves

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

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Integer Points 100%
  • Elliptic Curves 75%
  • Integral Solution 49%
  2 Scopus citations

• 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 journal › Article › peer-review

  • Hardy-Littlewood Method 100%
  • Finite Type 63%
  • Prime number 61%
  • Integer 32%
  • Form 25%
  3 Scopus citations

• 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 journal › Article › peer-review

  Open Access

  • Waring's problem 100%
  • Additive number Theory 98%
  • Natural number 62%
  • Form 27%
  • Theorem 27%
  2 Scopus citations
• 2013

  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 journal › Article › peer-review

  • Exceptional Sets 100%
  • Binary 59%
  • Diophantine equation 43%
  • Integer 41%
  • Asymptotic Formula 36%
  4 Scopus citations
• 2012

  Mean value theorems for binary Egyptian fractions II

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

  Research output: Contribution to journal › Article › peer-review
  4 Scopus citations
• 2011

  Inhomogeneous Diophantine approximation on planar curves

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

  Research output: Contribution to journal › Article › peer-review

  • Planar Curves 100%
  • Diophantine Approximation 96%
  • Simultaneous Approximation 48%
  • Rational Points 43%
  • Metric 26%
  18 Scopus citations

• Mean value theorems for binary Egyptian fractions

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

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Mean value theorem 100%
  • Vary 69%
  • Binary 61%
  • Diophantine equation 44%
  • Number of Solutions 44%
  8 Scopus citations
• 2008

  Local variation of euler products

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

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Euler Product 100%
  • Multiplicative Functions 45%
  • Dirichlet Series 41%
  • Mean Value 35%

• On the number of partitions into primes

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

  Research output: Contribution to journal › Article › peer-review

  • Logarithmic integral 100%
  • Partition 94%
  • Distribution of Primes 91%
  • Elementary Functions 73%
  • Beliefs 69%
  13 Scopus citations
• 2006

  Diophantine approximation on planar curves: The convergence theory

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

  Research output: Contribution to journal › Article › peer-review

  • Planar Curves 100%
  • Diophantine Approximation 96%
  • Convergence Theory 94%
  • Divergence 35%
  • Complement 30%
  61 Scopus citations
• 2005

  A variance for k-free numbers in arithmetic progressions

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

  Research output: Contribution to journal › Article › peer-review
  12 Scopus citations
• 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 journal › Article › peer-review

  Open Access

  • Dedekind zeta Function 100%
  • Abscissa 93%
  • Cubic Fields 92%
  • Mean value theorem 85%
  • Denote 42%
  1 Scopus citations

• 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 journal › Article › peer-review

  • Arithmetic sequence 100%
  • Moment 62%
  • Approximation 46%
  6 Scopus citations

• 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 journal › Article › peer-review

  • Arithmetic sequence 100%
  • Moment 62%
  • Approximation 46%
  6 Scopus citations
• 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 journal › Article › peer-review

• On a variance associated with the distribution of primes in arithmetic progressions

  Vaughan, R. C., May 2001, In: Proceedings of the London Mathematical Society. 82, 3, p. 533-553 21 p.

  Research output: Contribution to journal › Article › peer-review
  19 Scopus citations

• On sigma-PHI numbers

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

  Research output: Contribution to journal › Article › peer-review
  2 Scopus citations
• 2000

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

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

  Research output: Contribution to journal › Article › peer-review

  Open Access
  26 Scopus citations
• 1998

  Hardy's legacy to number theory

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

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Number theory 100%
  2 Scopus citations

• On a variance associated with the distribution of general sequences in arithmetic progressions. I

  Vaughan, R. C., Mar 15 1998, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 356, 1738, p. 781-791 11 p.

  Research output: Contribution to journal › Article › peer-review

  • progressions 100%
  • Arithmetic sequence 97%
  • Asymptotic Formula 82%
  • Modulus 75%
  • Class 26%
  12 Scopus citations

• On a variance associated with the distribution of general sequences in arithmetic progressions. II

  Vaughan, R. C., Mar 15 1998, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 356, 1738, p. 793-809 17 p.

  Research output: Contribution to journal › Article › peer-review

  • progressions 100%
  • Arithmetic sequence 97%
  • Asymptotic Formula 82%
  • Asymptotic distribution 77%
  • Modulus 75%
  12 Scopus citations

• 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 journal › Article › peer-review
  8 Scopus citations

• 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 journal › Article › peer-review

  • Exponential Sums 100%
  • Dissection 75%
  • Minor arc 75%
  • Generating Function 73%
  • Circle Method 62%
  18 Scopus citations
• 1997

  A special case of Vinogradov's mean value theorem

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

  Research output: Contribution to journal › Article › peer-review
  17 Scopus citations
• 1996

  On the eigenvalues of Redheffer's matrix, II

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

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Radius 100%
  • Eigenvalue 76%
  • Estimate 56%
  11 Scopus citations
• 1995

  Further improvements in Waring's problem

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

  Research output: Contribution to journal › Article › peer-review

  Open Access
  41 Scopus citations

• 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 journal › Article › peer-review
  29 Scopus citations

• Some Remarks on Gauss Sums Associated with Kth Powers

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

  Research output: Contribution to journal › Article › peer-review
  26 Scopus citations
• 1994

  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 journal › Article › peer-review
  13 Scopus citations
• 1991

  On a problem related to one of littlewood and offord

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

  Research output: Contribution to journal › Article › peer-review
  3 Scopus citations

• On waring’s problem: Some refinements

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

  Research output: Contribution to journal › Article › peer-review
  28 Scopus citations
• 1990

  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 journal › Article › peer-review
  35 Scopus citations

• 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 journal › Article › peer-review

  • Vector quantization 100%
  • Costs 34%
  1 Scopus citations