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On Vaughan's approximation: The first moment
Author(s) -
Fiorilli Daniel
Publication year - 2017
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12017
Subject(s) - moment (physics) , mathematics , range (aeronautics) , mathematical analysis , physics , quantum mechanics , materials science , composite material
We investigate the first moment of the difference between ψ ( x ; q , a ) and Vaughan's approximation in a certain range of q . We show that this last approximation is significantly more precise than the classical x / ϕ ( q ) , and that it captures the discrepancies of the distribution of primes in arithmetic progressions found in an earlier paper of the author.