Small gaps in coefficients of L-functions and B-free numbers in small   intervals
  We discuss questions related to the non-existence of gaps in the series defining modular forms and other arithmetic functions of various types, and improve results of Serre, Balog and Ono, and Alkan, using new results about exponential sums and the distribution of $B$-free numbers. 
Emmanuel Kowalski, Olivier Robert, Jie Wu