L-functions and modular forms

Research output

Research output per year 2014 2015 2016 2019

• 15 Article (Academic Journal)
• 1 Chapter in a book

Research output per year

Research output per year

Search results

• 2019

  A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

  Basor, E., Bleher, P., Buckingham, R., Grava, T., Its, A., Its, E. & Keating, J. P., 13 Sept 2019, In: Nonlinearity. 32, 10, p. 4033-4078 47 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Characteristic Polynomial 100%
  • Joint Moment 100%
  • Random Matrix 16%
  • Explicit Formula 16%
  • Matrix 16%
  14 Citations (Scopus)

  201 Downloads (Pure)

• Moments of zeta and correlations of divisor-sums: V

  Conrey, B. & Keating, J., 1 Apr 2019, In: Proceedings of the London Mathematical Society. 118, 4, p. 729-752 24 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Convolution 100%
  • Polynomial 100%
  • Sum of divisors 100%
  • Lower Order Term 50%
  • Critical Line 50%
  16 Citations (Scopus)

  280 Downloads (Pure)

• Variance of sums in arithmetic progressions of arithmetic functions associated with higher degree 0-functions in F_q[t]

  Roditty-Gershon, E., Hall, C. & Keating, J. P., 24 Dec 2019, In: International Journal of Number Theory. 16, 5, p. 1013-1030 18 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Variance 100%
  • Arithmetic Progression 100%
  • Arithmetic Function 100%
  • L-Function 66%
  • Matrix 33%
  155 Downloads (Pure)
• 2018

  Extreme values of CUE characteristic polynomials: A numerical study

  Fyodorov, Y. V., Gnutzmann, S. & Keating, J. P., 16 Nov 2018, In: Journal of Physics A: Mathematical and Theoretical. 51, 46, 23 p., 464001.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Characteristic Polynomial 100%
  • Numerical Analysis 100%
  • Extreme Value 100%
  • Eigenvalue 33%
  • Unitary Matrix 33%
  11 Citations (Scopus)

  179 Downloads (Pure)
• 2016

  Arithmetic Correlations Over Large Finite Fields

  Keating, J. P. & Roditty-Gershon, E., Mar 2016, In: International Mathematics Research Notices. 2016, 3, p. 860-874 15 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Finite Field 100%
  • Arithmetic Function 100%
  • Analytic Number Theory 50%
  • Function Field 50%
  • Von Mangoldt 50%
  4 Citations (Scopus)

  335 Downloads (Pure)

• Moments of zeta and correlations of divisor-sums: IV

  Conrey, B. & Keating, J. P., Dec 2016, In: Research in Number Theory. 2, 24 p., 24.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Convolution 100%
  • Polynomial 100%
  • Sum of divisors 100%
  • Lower Order Term 50%
  • Critical Line 50%
  21 Citations (Scopus)

  358 Downloads (Pure)

• On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class

  Bui, H. M., Keating, J. P. & Smith, D. J., 1 Aug 2016, In: Journal of the London Mathematical Society. 94, 1, p. 161-185 25 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Variance 100%
  • L-Function 100%
  • Arithmetic Function 100%
  • Riemann Zeta Function 50%
  • Mathematics 25%
  8 Citations (Scopus)

  341 Downloads (Pure)

• Pair correlation and twin primes revisited

  Conrey, B. & Keating, J. P., Oct 2016, In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472, 2194, 11 p., 20160548.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Analogy 15%
  5 Citations (Scopus)

  333 Downloads (Pure)

• Squarefree polynomials and möbius values in short intervals and arithmetic progressions

  Keating, J. P. & Rudnick, Z., 16 Mar 2016, In: Algebra and Number Theory. 10, 2, p. 375-420 46 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Arithmetic Progression 100%
  • Polynomial 100%
  • Integral 100%
  • Integer 50%
  • Variance 50%
  29 Citations (Scopus)

  355 Downloads (Pure)

• The Euclid-Mullin graph

  Booker, A. R. & Irvine, S., Aug 2016, In: Journal of Number Theory. 165, p. 30-57 28 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Euclid 100%
  • Structural Property 50%
  3 Citations (Scopus)

  290 Downloads (Pure)

• What is the probability that a random integral quadratic form in nvariables has an integral zero?

  Bhargava, M., Cremona, J. E., Fisher, T., Jones, N. G. & Keating, J. P., 9 Sept 2016, In: International Mathematics Research Notices. 2016, 12, p. 3828-3848 21 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Quadratic Form 100%
  • Probability Theory 100%
  • Rational Function 42%
  • Gaussian Distribution 28%
  • Random Matrix Theory 14%
  11 Citations (Scopus)

  284 Downloads (Pure)
• 2015

  Moments of zeta and correlations of divisor-sums: I

  Conrey, B. & Keating, J. P., 23 Mar 2015, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 373, 2040, 20140313.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Critical Line 100%
  • Polynomial 100%
  • Sum of divisors 100%
  29 Citations (Scopus)

  323 Downloads (Pure)

• Moments of zeta and correlations of divisor-sums: II

  Conrey, B. & Keating, J. P., 2015, Fields Institute Communications. Springer, New York, NY, Vol. 77. p. 75-85 11 p. (Fields Institute Communications; vol. 77).

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

  • Critical Line 100%
  • Riemann Zeta Function 100%
  • Polynomial 100%
  • Sum of divisors 100%
  23 Citations (Scopus)

• Moments of zeta and correlations of divisor-sums: III

  Conrey, J. B. & Keating, J. P., 1 Dec 2015, In: Indagationes Mathematicae. 26, 5, p. 736-747 12 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Polynomial 100%
  • Sum of divisors 100%
  • Lower Order Term 50%
  • Critical Line 50%
  • Riemann Zeta Function 50%
  26 Citations (Scopus)

  369 Downloads (Pure)

• Number fields and function fields: Coalescences, contrasts and emerging applications

  Keating, J. P., Rudnick, Z. & Wooley, T. D., 28 Apr 2015, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 373, 2040, 4 p., 20140315.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Function Field 100%
  • Finite Field 66%
  • Analytic Number Theory 33%
  • Irreducible Polynomial 33%
  • Arithmetic 33%
  2 Citations (Scopus)

  426 Downloads (Pure)
• 2014

  Zeros of L-functions outside the critical strip

  Booker, A. R. & Thorne, F., Dec 2014, In: Algebra and Number Theory. 8, 9, p. 2027-2042 16 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • L-Function 100%
  • Critical Strip 100%
  • Zero of L-Function 100%
  • Modular Form 50%
  • Dirichlet Series 50%
  7 Citations (Scopus)

  270 Downloads (Pure)