## A record of gremlin achievement

These errors survive in the 3nd printing. Errors of punctuation and of English are omitted, since the reader will be easily able to supply the correction her- or himself.
• Page 46. Line 3 of the proof of Lemma 2.1: the multiplication dot should be raised above the line of the bottom of the letters. (thanks to Nicolai Vorobjov, University of Bath).
• Page 52. Proof (sketch). Replace the pompous but inaccurate `though it would be a remarkable first-year undergraduate...' by `since 2p (p) = p^2 + p^2'. (thanks to Ewart Shaw of the University of Warwick, England).
• Page 69. This equation is missing something crucial. Append the symbols `=0', (thanks to Charles Cruickshank).
• Page 82. Line 2 Replace log(nx) by log(x^n). (Thanks to Andriy Oliinyk of Toronto, Canada).
• Page 82. Definition 3.11. The quantity e is not a natural number (thanks to my colleague Edward Fraenkel of the University of Bath).
• Page 91. 5th paragraph. x=y=e^(2*pi*i/3) so xy=e^(4*pi*i/3)=e^(-2*pi*i/3). (Andriy Oliinyk).
• Page 197-198, Proposition 7.2 and the preamble. This is not an error, but a matter of mathematical hygiene. It would have been better to define f(0) to be the gcd of 0 and 1, and so f(0)=1. With this variation f would be (just when you thought that it was safe to get back into the water) continuous at all irrational points and discontinuous at all rational points (thanks to my colleague Geoffrey Burton of the University of Bath).
If you find an unrecorded glitch in the book, please send an email to G.C.Smith@bath.ac.uk and get yourself thanked here and in any reprinted edition.