Fredrik Johansson

Fredrik Johansson


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I'm a researcher at INRIA Bordeaux and Institut de Mathématiques de Bordeaux, working in the LFANT team headed by Andreas Enge. My research is centered on computer algebra and rigorous numerical computing. I'm especially interested in fast and reliable algorithms for arbitrary-precision arithmetic, complex analysis, and numerical evaluation of special functions (including hypergeometric functions, L-functions, and modular forms).

Interested in doing a master's thesis or PhD in this area? Feel free to contact me. (No guarantees that funding will be available.)

Mathematical software

A big part of my work is to develop free scientific software.


This list is available in BibTeX format (txt file). I also have a Google Scholar profile.

  1. Faster arbitrary-precision dot product and matrix multiplication
    26th IEEE Symposium on Computer Arithmetic (ARITH26), 2019. [arXiv] [HAL]
  2. Numerical evaluation of elliptic functions, elliptic integrals and modular forms
    Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Springer, 2019, pp. 269-293. [arXiv] [HAL] [DOI]
  3. Computing Stieltjes constants using complex integration
    With Iaroslav V. Blagouchine. Mathematics of Computation, vol 88, 2019, pp. 1829-1850. [arXiv] [HAL] [DOI]
  4. Numerical integration in arbitrary-precision ball arithmetic
    Mathematical Software - ICMS 2018, Springer LNCS, 2018, pp. 255-263. [arXiv] [HAL] [DOI]
  5. Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights
    With Marc Mezzarobba. SIAM Journal on Scientific Computing 40(6), 2018, pp. C726-C747. [arXiv] [HAL] [DOI]
  6. Computing the Lambert W function in arbitrary-precision complex interval arithmetic
    Numerical Algorithms, 2019 (to appear). [arXiv] [HAL] [DOI]
  7. Nemo/Hecke: computer algebra and number theory packages for the Julia programming language
    With Claus Fieker, William Hart and Tommy Hofmann. 42nd International Symposium on Symbolic and Algebraic Computation (ISSAC'17), 2017, pp. 157-164. [arXiv] [HAL]
  8. Arb: efficient arbitrary-precision midpoint-radius interval arithmetic
    IEEE Transactions on Computers, vol 66, issue 8, 2017, pp. 1281-1292. [DOI] [PDF] [arXiv] [HAL]
  9. Short addition sequences for theta functions
    With Andreas Enge and William Hart. Journal of Integer Sequences, vol 21, 2018, article 18.2.4. [arXiv] [HAL]
  10. Computing hypergeometric functions rigorously
    ACM Transactions on Mathematical Software, 2019 (to appear). [PDF] [arXiv] [HAL]
  11. SymPy: Symbolic computing in Python
    With Aaron Meurer et al. PeerJ Computer Science 3:e103, 2017. [DOI] [HAL]
  12. Efficient implementation of elementary functions in the medium-precision range
    22nd IEEE Symposium on Computer Arithmetic (ARITH22), 2015, pp. 83-89. [PDF] [arXiv] [DOI]
  13. A bound for the error term in the Brent-McMillan algorithm
    With Richard P. Brent. Mathematics of Computation, vol 84, 2015, pp. 2351-2359. [PDF] [arXiv] [DOI]
  14. A fast algorithm for reversion of power series
    Mathematics of Computation, vol 84, 2015, pp. 475-484. [PDF] [arXiv] [DOI] [info]
  15. Fast and rigorous computation of special functions to high precision
    PhD thesis, RISC, Johannes Kepler University, Linz, 2014. [PDF] [info]
  16. Evaluating parametric holonomic sequences using rectangular splitting
    39th International Symposium on Symbolic and Algebraic Computation (ISSAC'14), 2014, pp. 256-263. [PDF] [slides] [arXiv] [DOI] [info]
  17. Using functional equations to enumerate 1324-avoiding permutations
    With Brian Nakamura. Advances in Applied Mathematics, vol 56, 2014, pp. 20-34. [PDF] [arXiv] [DOI] [info]
  18. Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
    Numerical Algorithms, vol 69, issue 2, 2015, pp. 253-270. [PDF] [arXiv] [DOI] [info]
  19. Ore polynomials in Sage
    With Manuel Kauers and Maximilian Jaroschek. Computer Algebra and Polynomials, Springer LNCS, 2015, pp. 105-125. [PDF] [arXiv] [DOI] [info]
  20. Arb: a C library for ball arithmetic
    ACM Communications in Computer Algebra, vol 47, issue 4, December 2013, pp. 166-169. [PDF] [slides] [DOI] [info]
    Note: the 2017 IEEE TC paper largely supersedes this extended abstract.
  21. Finding hyperexponential solutions of linear ODEs by numerical evaluation
    With Manuel Kauers and Marc Mezzarobba. 38th International Symposium on Symbolic and Algebraic Computation (ISSAC'13), 2013, pp. 211-218. [PDF] [arXiv] [DOI] [info]
  22. Efficient implementation of the Hardy-Ramanujan-Rademacher formula
    LMS Journal of Computation and Mathematics, vol 15, 2012, pp. 341-359. [PDF] [arXiv] [DOI] [info]
  23. Simulation of the Maxwell-Dirac and Schrödinger-Poisson systems
    Master's thesis, Chalmers University of Technology, Gothenburg, 2010.

Erdős number

My Erdős number is 3 (0-1, 1-2, 2-3).



Academic history

Other professional activity

Conference organization


I've reviewed papers for a number of journals and conferences, including Mathematics of Computation, Journal of Symbolic Computation, Numerical Algorithms, BIT Numerical Mathematics, Advances in Applied Mathematics, Mathematics, ACM Transactions on Mathematical Software, IEEE Transactions on Circuits and Systems, IEEE Transactions on Computers.

Summers of code

I've taken part in Google Summer of Code once as a student and three times as a mentor:

In summer 2009 and 2010, I worked on Sage and mpmath as a contractor for the American Institute of Mathematics, thanks to funding provided by William Stein.

Unprofessional activity


Doom levels

My old Doom maps and related information.