Resumen de The sum-of-digits function of squares

Michael Drmota , Joël Rivat

• The set of squares , , is considered and the sum of binary digits is split up into two parts , where collects the first digits and collects the remaining digits. Very precise results on the distribution of and are presented. For example, asymptotic formulae are provided for the numbers and and it is shown that these partial sum-of-digits functions are asymptotically equidistributed in residue classes. These results are prompted by a conjecture by Gelfond saying that the (total) sum-of-digits function is asymptotically equidistributed in residue classes.