The editors of Mathematika are pleased to announce a special issue of the journal dedicated to Klaus Friedrich Roth, which is now available on Cambridge Core. Roth, who passed away on 10 November 2015 at age 90, published during his distinguished career five papers in Mathematika, including three of his most influential.

  1. The 1955 paper `Rational approximations to algebraic numbers‘ was his legendary solution of the famous Siegel conjecture concerning approximation of algebraic numbers by rationals, for which he was awarded the Fields Medal in 1958.
  2. The 1965 paper `On the large sieves of Linnik and Rényi‘ was a huge breakthrough and, together with the almost contemporaneous paper of Bombieri published also in Mathematika in the same year, continues to have a profound impact on the development of analytic number theory today.
  3. The 1954 paper `On irregularities of distribution‘, although cited much less than the other two, was nevertheless considered by Roth to be his best work, and paved the way for what is now known as geometric discrepancy theory, a subject at the crossroads of harmonic analysis, combinatorics, approximation theory, probability theory and even group theory.

The editors of Mathematika resolved in early 2016 to dedicate an issue of the journal to celebrate the life and work of Roth. William Chen and Robert Vaughan act as special editors for this project and, thanks to their efforts, many excellent contributions were received from friends and colleagues of Roth, making this a very special issue.

It was a coincidence that the famous abc-conjecture was first formulated in an open problem session during the Symposium on Analytic Number Theory held at Imperial College in 1985 on the occasion of Roth’s sixtieth birthday. As no formal proceedings were published and the very brief records were only available to the participants of the symposium, this has caused much inconvenience to the many authors who wish to cite it.

The special editors have invited David Masser to write some brief anecdotes on this occasion. His note `Abcological anecdotes‘ opens this issue, and will serve as a reference point for this historical moment in the history of our subject.

All three of the above referenced papers are free to read through 31st January 2018.

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