Professor Andrew R Booker

Search results

• 2025

  Murmurations of modular forms in the weight aspect

  Bober, J. W., Booker, A. R., Lee, M. & Lowry-Duda, D., 11 Feb 2025, (Accepted/In press) In: Algebra and Number Theory.

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

  • Modular Form 100%
  • Eigenvalue 50%
  • Archimedean 50%
• 2023

  An extension of Venkatesh's converse theorem to the Selberg class

  Lee, M., Booker, A. R. & Farmer-Evans, M. F. M. F., 2023, In: Forum of Mathematics, Sigma. 11, 10 p., e26.

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

  Open Access

  • Trace Formula 100%
  • Modular Form 100%
  • Gamma Factor 100%
• 2022

  Primitive element pairs with a prescribed trace in the cubic extension of a finite field

  Booker, A. R., Cohen, S., Leong, N. & Trudgian, T., 25 Apr 2022, (E-pub ahead of print) In: Bulletin of the Australian Mathematical Society. 106, 3, p. 458-462 5 p.

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

  Open Access

  File

  • Finite Field 100%
  • Primitive Element 100%
  • Prime Power 25%
  2 Citations (Scopus)

  44 Downloads (Pure)

• Primitive elements with prescribed traces

  Booker, A. R., Cohen, S., Trudgian, T. & Leong, N., 1 Dec 2022, In: Finite Fields and Their Applications. 84, 102094.

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

  Open Access
  3 Citations (Scopus)
• 2021

  On a question of Mordell

  Booker, A. R. & Sutherland, A., 16 Mar 2021, In: Proceedings of the National Academy of Sciences of the United States of America. 118, 11, 11 p., e2022377118.

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

  Open Access

  File

  • Charity 100%
  • Solution and Solubility 100%
  8 Citations (Scopus)

  200 Downloads (Pure)

• On a Recursively Defined Sequence Involving the Prime Counting Function

  Alkan, A., Booker, A. R. & Luca, F., 31 Jan 2021, In: Journal of Integer Sequences. 24, 18 p., 21.3.1.

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

  Open Access

  File

  • Sequences 100%
  • Number 25%
  134 Downloads (Pure)

• Wolstenholme and Vandiver primes

  Booker, A. R., Hathi, S., Mossinghoff, M. & Trudgian, T., 30 Jun 2021, (E-pub ahead of print) In: Ramanujan Journal.

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

  Open Access
• 2020

  Test vectors for Rankin–Selberg L-functions

  Booker, A. R., Krishnamurthy, M. & Lee, M., 1 Apr 2020, In: Journal of Number Theory. 209, p. 37-48 12 p.

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

  Open Access

  File

  • L-Function 100%
  • Integral 100%
  4 Citations (Scopus)

  81 Downloads (Pure)

• Twist-minimal trace formulas and the Selberg eigenvalue conjecture

  Booker, A. R., Lee, M. & Strömbergsson, A., 1 Dec 2020, In: Journal of the London Mathematical Society.

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

  Open Access

  File

  • Eigenvalue 100%
  • Trace Formula 100%
  • Conditionals 50%
  • Apply It 50%
  • Selberg Trace Formula 50%
  5 Citations (Scopus)

  101 Downloads (Pure)
• 2019

  A converse theorem without root numbers

  Booker, A., 21 May 2019, In: Mathematika. 65, 4, p. 862-873 12 p.

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

  Open Access

  File

  • L-Function 100%
  • Functional Equation 100%
  1 Citation (Scopus)

  198 Downloads (Pure)

• A note on Maass forms of icosahedral type

  Booker, A. R., 1 Aug 2019, In: Mathematische Zeitschrift. 292, 3-4, p. 1315-1324 10 p.

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

  Open Access

  File

  • Fourier Coefficient 100%
  • Concludes 50%
  • Galois Representation 50%
  • Symmetric Power 50%
  • Density Theorem 50%
  264 Downloads (Pure)

• Cracking the problem with 33

  Booker, A. R., 1 Sept 2019, In: Research in Number Theory. 5, 3, 6 p., 26.

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

  Open Access

  File

  • Solution and Solubility 100%
  13 Citations (Scopus)

  585 Downloads (Pure)

• Quantitative estimates for simple zeros of L-functions

  Booker, A., Milinovich, M. B. & Ng, N., Feb 2019, In: Mathematika. 65, 2, p. 375-399 25 p.

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

  Open Access

  File

  • L-Function 100%
  • Modular Form 100%
  • Zero of L-Function 100%
  1 Citation (Scopus)

  182 Downloads (Pure)

• Simple zeros of automorphic L-functions

  Booker, A., Cho, P. & Kim, M., Jun 2019, In: Compositio Mathematica. 155, 6, p. 1224-1243 20 p.

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

  Open Access

  File

  • L-Function 100%
  • Automorphic Representation 50%
  5 Citations (Scopus)

  182 Downloads (Pure)

• Subconvexity for modular form L-functions in the t aspect

  Booker, A. R., Milinovich, M. B. & Ng, N., 7 Jan 2019, In: Advances in Mathematics. 341, p. 299-335 37 p.

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

  Open Access

  File

  • L-Function 100%
  • Modular Form 100%
  • Cusp Form 50%
  • Modular Group 50%
  • Summation 50%
  13 Citations (Scopus)

  170 Downloads (Pure)

• Turing’s Method for the Selberg Zeta-Function

  Booker, A. & Platt, D. J., 24 Jan 2019, In: Communications in Mathematical Physics. 365, 1, p. 295-328 34 p.

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

  Open Access

  File

  • Selberg Zeta Function 100%
  • Riemann Zeta Function 50%
  1 Citation (Scopus)

  320 Downloads (Pure)
• 2018

  A conjectural extension of Hecke’s converse theorem

  Bettin, S., Bober, J., Booker, A., Conrey, B., Lee, M., Molteni, G., Oliver, T., Platt, D. J. & Steiner, R., Dec 2018, In: Ramanujan Journal. 47, 3, p. 659-684 26 p.

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

  Open Access

  File

  • Characters 100%
  6 Citations (Scopus)

  348 Downloads (Pure)

• Finite connected components of the aliquot graph

  Booker, A. R., 2018, In: Mathematics of Computation. 87, 314, p. 2891-2902 12 p.

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

  Open Access

  File

  • Connected Component 100%
  • Conditionals 50%
  • Goldbachs Conjecture 50%
  • Even number 50%
  • Inverse Image 50%
  4 Citations (Scopus)

  484 Downloads (Pure)

• Primitive values of quadratic polynomials in a finite field

  Booker, A., Cohen, S., Sutherland, N. & Trudgian, T., 30 Oct 2018, (E-pub ahead of print) In: Mathematics of Computation. 10 p.

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

  Open Access

  File

  • Finite Field 100%
  • Quadratic Polynomial 100%
  • Primitive Root 100%
  16 Citations (Scopus)

  296 Downloads (Pure)

• Rapid computation of L-functions attached to Maass forms

  Booker, A. R. & Then, H. L., Jun 2018, In: International Journal of Number Theory. 14, 5, p. 1459-1485 27 p.

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

  Open Access

  File

  • L-Function 100%
  • Critical Line 50%
  • Cusp Form 50%
  • Consecutive Zero 50%
  3 Citations (Scopus)

  159 Downloads (Pure)
• 2017

  Squarefree smooth numbers and Euclidean prime generators

  Booker, A. R. & Pomerance, C., 1 Dec 2017, In: Proceedings of the American Mathematical Society. 145, 12, p. 5035-5042 8 p.

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

  Open Access

  File

  • Prime Factor 100%
  • Euclid 100%
  3 Citations (Scopus)

  367 Downloads (Pure)

• The Selberg trace formula as a Dirichlet series

  Booker, A. R. & Lee, M., May 2017, In: Forum Mathematicum. 29, 3, p. 519-542 24 p.

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

  Open Access

  File

  • Dirichlet Series 100%
  • Selberg Trace Formula 100%
  • L-Function 33%
  • Weighted Sum 33%
  3 Citations (Scopus)

  347 Downloads (Pure)
• 2016

  A converse theorem for GL(n)

  Booker, A. R. & Krishnamurthy, M., 25 Jun 2016, In: Advances in Mathematics. 296, p. 154-180 27 p.

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

  Open Access

  File

  • Automorphic Representation 100%
  • Data Analytics 100%
  2 Citations (Scopus)

  277 Downloads (Pure)

• A database of genus-2 curves over the rational numbers

  Booker, A. R., Sijsling, J., Sutherland, A. V., Voight, J. & Yasaki, D., 2016, In: LMS Journal of Computation and Mathematics. 19, A, p. 235-254 20 p.

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

  Open Access

  File

  • L-Function 100%
  • Rational Number 100%
  • Modular Form 50%
  30 Citations (Scopus)

  486 Downloads (Pure)

• A variant of the Euclid-Mullin sequence containing every prime

  Booker, A. R., 4 Jul 2016, In: Journal of Integer Sequences. 19, 6, 6 p., 4.

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

  Open Access

  File

  • Euclid 100%
  • Prime Number 33%
  3 Citations (Scopus)

  80 Downloads (Pure)

• Simple zeros of degree 2 L-functions

  Booker, A. R., Apr 2016, In: Journal of the European Mathematical Society. 18, 4, p. 813-823 11 p.

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

  Open Access

  File

  • L-Function 100%
  4 Citations (Scopus)

  280 Downloads (Pure)

• Square-free values of reducible polynomials

  Booker, A. & Browning, T., 1 Jun 2016, In: Discrete Analysis. 2016, 8, 16 p.

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

  Open Access

  File

  • Divisor 39%
  • Calculate 27%
  6 Citations (Scopus)

  357 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)

  311 Downloads (Pure)
• 2015

  Detecting squarefree numbers

  Booker, A. R., Hiary, G. & Keating, J. P., 30 Jan 2015, In: Duke Mathematical Journal. 164, 2, p. 235-275 41 p.

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

  Open Access

  File

  • Integer 100%
  • Explicit Formula 100%
  • Conditionals 100%
  • L-Function 100%
  • Riemann Hypothesis 100%
  9 Citations (Scopus)

  386 Downloads (Pure)

• L-functions as distributions

  Booker, A., 8 Feb 2015, In: Mathematische Annalen. 363, 1, p. 423-454 32 p.

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

  Open Access

  File

  • L-Function 100%
  • Explicit Formula 33%
  • Functional Equation 33%
  • Analytic Continuation 33%
  • Automorphic Representation 33%
  6 Citations (Scopus)

  285 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)

  280 Downloads (Pure)
• 2013

  Bounds and algorithms for the K-Bessel function of imaginary order

  Booker, A. R., Strömbergsson, A. & Then, H. L., 2013, In: LMS Journal of Computation and Mathematics. 16, p. 78-108 31 p.

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

  Open Access

  File

  • Asymptotics 100%
  • Modified Bessel Function 100%
  • Convergent Series 100%
  • Steepest Descent 100%
  • Bessel Function 100%
  8 Citations (Scopus)

  343 Downloads (Pure)

• Further refinements of the GL(2) converse theorem

  Booker, A. R. & Krishnamurthy, M., Oct 2013, In: Bulletin of the London Mathematical Society. 45, 5, p. 987-1003 17 p.

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

  Open Access

  File

  • Eisenstein Series 100%
  2 Citations (Scopus)

  387 Downloads (Pure)

• Weil's converse theorem with poles

  Booker, A. & Krishnamurthy, M., 2013, In: International Mathematics Research Notices. 2014, 19, p. 5328–5339 10 p.

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

  Open Access

  File

  • Characters 100%
  8 Citations (Scopus)

  573 Downloads (Pure)
• 2012

  On Mullin's second sequence of primes

  Booker, A., 2012, In: Integers. 8 p.

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

  • Prime Number 100%
  • Euclid 100%
  • Omits 100%
• 2011

  A strengthening of the GL(2) converse theorem

  Booker, A. & Krishnamurthy, M., May 2011, In: Compositio Mathematica. 147, 3, p. 669 - 715 47 p.

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

  • L-Function 100%
  11 Citations (Scopus)
• 2008

  Uncovering a new L-function

  Booker, A., 2008, In: Notices of the American Mathematical Society. 55, issue 9, p. 1088 - 1094 7 p.

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

  • L-Function 100%
  • Riemann Zeta Function 33%
  • Polynomial 33%
  • Entire Function 33%
  • Complex Variable Function 33%
  5 Citations (Scopus)
• 2007

  Numerical computations with the trace formula and the Selberg eigenvalue conjecture

  Booker, A. & Strömbergsson, A., Jun 2007, In: Journal für die reine und angewandte Mathematik. 2007 (607), p. 113 - 161 49 p.

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

  • Eigenvalue 100%
  • Trace Formula 100%
  • Numerical Computation 100%
  • Selberg Trace Formula 33%
  • Galois Representation 33%
  21 Citations (Scopus)
• 2006

  Artin's conjecture, Turing's method, and the Riemann hypothesis

  Booker, A., Dec 2006, In: Experimental Mathematics. 15 (4), p. 385 - 407 24 p.

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

  • Riemann Hypothesis 100%
  • L-Function 50%
  • Zeta-Functions 50%
  • Trace Formula 25%
  • Explicit Formula 25%
  25 Citations (Scopus)

• Effective computation of Maass cusp forms

  Booker, A., Strömbergsson, A. & Venkatesh, A., Jun 2006, In: International Mathematics Research Notices. 2006 (71281), p. 1 - 34 34 p., Art no 71281.

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

  • Eigenvalue 100%
  • Cusp Form 100%
  • Laplace Operator 50%
  • Decimal Place 50%
  • Transcendentals 25%
  37 Citations (Scopus)

• Quadratic class numbers and character sums

  Booker, A., Jul 2006, In: Mathematics of Computation. 75 (255), p. 1481 - 1492 12 p.

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

  • Character Sum 100%
  • Correct Answer 50%
  18 Citations (Scopus)

• Turing and the Riemann Hypothesis

  Booker, A., Nov 2006, In: Notices of the American Mathematical Society. 53 (10), p. 1208 - 1211 4 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  12 Citations (Scopus)
• 2005

  Numerical tests of modularity

  Booker, A., Dec 2005, In: Journal of the Ramanujan Mathematical Society. 20 (4), p. 283 - 339 57 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
• 2003

  Poles of Artin L-functions and the strong Artin conjecture

  Booker, A., Nov 2003, In: Annals of Mathematics. 158 (3), p. 1089 - 1098 10 p.

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

  • L-Function 100%
  • Galois Representation 50%
  • Irreducibles 50%
• 2000

  A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman

  Booker, A., 2000, In: Experimental Mathematics. 9 (4), p. 571 - 581 11 p.

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

  • Eigenvalue 100%
  • Kloosterman Sum 100%
  • Fourier Coefficient of Automorphic Forms 100%
  • Fourier Coefficient 100%
  9 Citations (Scopus)