OAI/NumberTheory/TotientAsymptotic/PublishedConcentration.lean
6 declarations, 0 contain sorry, 0 declared as axioms
The fixed-deviation consequence of Ford, The distribution of totients,
arXiv:1104.3264v2 (2013), Lemma 6.1, (6.6)--(6.8), pp. 30--31.
We use deviation 1/40 only. For the lower tail take
theta = (1/40)/(1-1/40) in (6.6); for the upper tail take
theta = -(1/40)/(1+1/40) in (6.7) or (6.8), splitting at
-i*lambda_i/L. The uniform bounds (6.4) give positive absolute
constants in exp (-c*(L-i)). Letting the terminal cutoff decrease to
zero and rescaling the simplex gives precisely the input below.
The transfer from Ford's terminal coefficient 1 to our coefficient a_1
is proved here using shrinkLast, rather than assumed in this input.
- def
OAI.TotientAsymptotic.fordSimplexCenterline 23 - def
OAI.TotientAsymptotic.fordCoordinateBadline 26 - def
OAI.TotientAsymptotic.FordCoordinateConcentrationInputline 29 - lemma
OAI.TotientAsymptotic.measurableSet_fordCoordinateBadline 35 - lemma
OAI.TotientAsymptotic.prefixRegion_volume_ne_topline 40 - theorem
OAI.TotientAsymptotic.simplex_coordinate_concentrationline 45