A Short Note on the Bruinier-Kohnen Sign Equidistribution Conjecture and   Hal\'asz' Theorem
  In this note, we improve earlier results towards the Bruinier-Kohnen sign equidistribution conjecture for half-integral weight modular eigenforms in terms of natural density by using a consequence of Hal\'asz' Theorem. Moreover, applying a result of Serre we remove all unproved assumptions. 
Ilker Inam and Gabor Wiese
math.NT