Fredrik Johansson

Fredrik Johansson


Postdoc, LFANT, INRIA / IMB, Bordeaux.


My main research topic is arbitrary-precision arithmetic and computation of special functions (hypergeometric functions, the gamma function, the Riemann zeta function, and so forth). I work on developing algorithms that are efficient (both asymptotically and in practice) and also reliable, ideally with provably correct error bounds. More broadly, I'm interested in polynomial arithmetic, numerical analysis, computer algebra, computational number theory, and implementation aspects of mathematical software. I'm the main author of Arb and mpmath, and coauthor of FLINT.

My record computation of the partition function is a fun, if not very practically useful, achievement. While my own work is largely theoretical, software that I developed has found use by others in diverse applications such as stellar astrophysics, quantum field theory, antenna design, image processing, computational biology, and free-space optical communication.

Since September 2014, I'm a postdoc at INRIA Bordeaux-Sud-Ouest and Institut de Mathématiques de Bordeaux, working in the LFANT project-team headed by Andreas Enge and Karim Belabas. From 2010 to 2014, I did my PhD in symbolic computation at RISC, Linz, where Manuel Kauers was my advisor. I have an MSc in engineering physics from Chalmers University of Technology, Gothenburg. I was born in Sweden.



This list is also available in BibTeX format (txt file).

  1. F. Johansson. Efficient implementation of elementary functions in the medium-precision range. 22nd IEEE Symposium on Computer Arithmetic (ARITH22), 2015, 83-89. [PDF] [arXiv] [DOI]
  2. R. P. Brent, F. Johansson. A bound for the error term in the Brent-McMillan algorithm. Mathematics of Computation, vol 84, 2015, 2351-2359. [PDF] [arXiv] [DOI]
  3. F. Johansson. A fast algorithm for reversion of power series. Mathematics of Computation, vol 84, 2015, 475-484. [PDF] [arXiv] [DOI] [info]
  4. F. Johansson. Fast and rigorous computation of special functions to high precision. PhD thesis, RISC, Johannes Kepler University, Linz, 2014. [PDF] [info]
  5. F. Johansson. Evaluating parametric holonomic sequences using rectangular splitting. ISSAC 2014, 256-263. [PDF] [slides] [arXiv] [DOI] [info]
  6. F. Johansson, B. Nakamura. Using functional equations to enumerate 1324-avoiding permutations. Advances in Applied Mathematics, vol 56, 2014, 20-34. [PDF] [arXiv] [DOI] [info]
  7. F. Johansson. Rigorous high-precision computation of the Hurwitz zeta function and its derivatives. Numerical Algorithms, 2014. [PDF] [arXiv] [DOI] [info]
  8. M. Kauers, M. Jaroschek, F. Johansson. Ore polynomials in Sage. Computer Algebra and Polynomials, 2015, 105-125, Springer Lecture Notes in Computer Science. [PDF] [arXiv] [DOI] [info]
  9. F. Johansson. Arb: a C library for ball arithmetic. ACM Communications in Computer Algebra, vol 47, issue 4, December 2013, 166-169. [PDF] [slides] [DOI] [info]
  10. F. Johansson, M. Kauers, M. Mezzarobba. Finding hyperexponential solutions of linear ODEs by numerical evaluation. ISSAC 2013, 211-218. [PDF] [arXiv] [DOI] [info]
  11. F. Johansson. Efficient implementation of the Hardy-Ramanujan-Rademacher formula. LMS Journal of Computation and Mathematics, vol 15, 2012, 341-359. [PDF] [arXiv] [DOI] [info]

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

Mathematical software

I've taken part in Google Summer of Code once as a student and twice 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.