Fredrik Johansson

Fredrik Johansson


I'm a mathematician at INRIA Bordeaux-Sud-Ouest and Institut de Mathématiques de Bordeaux, working in the LFANT team headed by Andreas Enge. My research interests include arbitrary-precision arithmetic, interval arithmetic, computational number theory, computer algebra, and special functions.

I'm a permanent researcher (CR2) at INRIA since October 2015, after previously having been employed as a postdoc for one year. From October 2010 to March 2014, I did my PhD in symbolic computation at RISC in Linz, Austria, where Manuel Kauers was my advisor. I grew up in Sweden, and have an MSc (2010) in engineering physics from Chalmers University of Technology, Gothenburg.


I'm interested in computer algebra, in the broad sense meaning software and algorithms for doing mathematics. I've come to focus on two aspects:

In particular, I've been working quite extensively on methods for computing special functions (hypergeometric functions, the gamma function, the Riemann zeta function, modular forms, and so forth) with arbitrary precision and rigorous error bounds.

I care a lot about developing practical, robust and maintainable free software. My central project over the last couple of years has been to create Arb, a C library for arbitrary-precision interval arithmetic (and much more besides basic arithmetic) using an efficient midpoint-radius representation of real numbers. I'm also the main author of the arbitrary-precision Python library mpmath, and coauthor of the C library FLINT which does number theory and fast arithmetic over many exact domains. All three libraries are standard components of SageMath. See below for other software I've contributed to.

My record computation of the partition function is a fun, if not very practically useful, achievement. Software that I developed has been cited by other scientists in well over 100 papers, in applications such as stellar astrophysics, quantum field theory, antenna design, image processing and computational biology.



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 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.