Kevin Ford
Published 2011-04-16, updated 2013-07-14Version 2
New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for V_k(x) (see the paragraph after (5.20)), fixed the statement and proof of Theorem 3. New, precise way to relate sums to volumes (Lemmas 3.1, 3.9) and provided full details in Section 6 of the proofs of Theorems 10-13. Slightly different versions of Theorems 10,11,12,14 (qualitatively the same) with simpler proofs. Sections 7 and 8 combined (new section 7). A few definitions, such as S-normal, changed slightly. Some reorganization of material.
Comments: very minor revision: Corrected statement of Lemma 7.2 and following comments
Journal: (original version) Ramanujan J. 2 (1998), 67-151
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average
On the distribution of matrix elements for the quantum cat map
Gaps between zeros of $ζ(s)$ and the distribution of zeros of $ζ'(s)$
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