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Exponential Sums and Lattice Points
Author(s) -
Huxley M. N.
Publication year - 1993
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-66.1.70-s
Subject(s) - mathematics , combinatorics , logarithm , sign (mathematics) , exponential function , lemma (botany) , discrete mathematics , arithmetic , mathematical analysis , ecology , poaceae , biology
Page 476. Correct section number from 23 to 3. Pages 479–480. The first minus sign in the expression for g(x) should be plus. The author's idiotic proof‐reading has led to the false sign being repeated twice on p. 480. Pages 480–481. The number x 1 depends on h , so it should be called x hl The differencing argument on p. 481 should be applied in h , with h in a fixed residue class mode q . This makes the error term larger by a factor of q/R , which is acceptable. Page 484. In the definition of the vector y (j) , insert a square‐root sign so that the fourth entry is − K J times the third entry. Page 486. The logarithm power in (6.5) should be log 8 N . However, the binary expansion argument need only be done in the summand l , since the sum over k is treated by Lemma 2.4 at the foot of the page. This simplification brings the logarithm power in (6.5) back down to log 4 N . Page 497. The sentence ending in (8.15) is wrong; see the comments in [1].