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Jan 19, 2021 at 7:00 comment added Seva @fedja: For the first remark, the answer is "yes"; any other typos, to fix them all together? For the second remark - yes, as far as I can see, using Fejer's kernel saves the logarithm.
Jan 18, 2021 at 17:28 comment added fedja I believe that it should be $\chi(a^{-1}z){\color{red}\psi(z)}$ in the rearranged sum and it looks like that if we use the Fejer kernel instead of the Dirichlet one, we can kill the $\log p$ factor. Am I right?
Jan 18, 2021 at 7:51 history edited Seva CC BY-SA 4.0
A typo fixed
Jan 18, 2021 at 2:16 vote accept fedja
Jan 18, 2021 at 2:16 comment added fedja Thanks! It looks nice, indeed. Thanks to @MarkLewko too for pointing out how to improve the elementary counting argument (though "elementary" stops being "trivial" in that improvement) :-) Anyway, the question has been completely answered, so I'll push the "accept" button. However, if someone still wants to add something in comments or another answer, that will be always welcome.
Jan 17, 2021 at 11:20 history edited Seva CC BY-SA 4.0
added 20 characters in body
Jan 16, 2021 at 8:25 history answered Seva CC BY-SA 4.0