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).

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. Preprint, 2019, submitted. [arXiv] [HAL]
  2. Numerical evaluation of elliptic functions, elliptic integrals and modular forms. Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, 269-293, Springer, 2019. [arXiv] [HAL] [DOI]
  3. Computing Stieltjes constants using complex integration. With Iaroslav V. Blagouchine. Mathematics of Computation, 2019. [arXiv] [HAL] [DOI]
  4. Numerical integration in arbitrary-precision ball arithmetic. Mathematical Software - ICMS 2018, 255-263. Springer Lecture Notes in Computer Science, 2018. [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), C726-C747, 2018. [arXiv] [HAL] [DOI]
  6. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. Numerical Algorithms, 2019. [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. ISSAC 2017. [arXiv] [HAL]
  8. Arb: efficient arbitrary-precision midpoint-radius interval arithmetic. IEEE Transactions on Computers, vol 66, issue 8, 2017, 1281-1292. [DOI] [PDF] [arXiv] [HAL] Highlighted paper, IEEE TC Special Section on Computer Arithmetic.
  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. Preprint, June 2016, submitted. [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, 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, 2351-2359. [PDF] [arXiv] [DOI]
  14. A fast algorithm for reversion of power series. Mathematics of Computation, vol 84, 2015, 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. ISSAC 2014, 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, 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, 253-270. [PDF] [arXiv] [DOI] [info]
  19. Ore polynomials in Sage. With Manuel Kauers and Maximilian Jaroschek. Computer Algebra and Polynomials, 2015, 105-125, Springer Lecture Notes in Computer Science. [PDF] [arXiv] [DOI] [info]
  20. Arb: a C library for ball arithmetic. ACM Communications in Computer Algebra, vol 47, issue 4, December 2013, 166-169. [PDF] [slides] [DOI] [info] Winner of the ISSAC 2013 Distinguished Software Presentation Award. Note: this extended abstract has largely been superseded by the 2017 IEEE TC paper.
  21. Finding hyperexponential solutions of linear ODEs by numerical evaluation. With Manuel Kauers and Marc Mezzarobba. ISSAC 2013, 211-218. [PDF] [arXiv] [DOI] [info]
  22. Efficient implementation of the Hardy-Ramanujan-Rademacher formula. LMS Journal of Computation and Mathematics, vol 15, 2012, 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.

Trivia: my Erdős number is 3 (0-1, 1-2, 2-3).


Academic history

Other professional and academic activity

I've helped organize some conferences and workshops:

I've reviewed papers for a number of journals, 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.

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.



My Doom maps and related information.