Congruences for a mock modular form on ${\mathrm{SL}}_2(\mathbb{Z})$ and the smallest parts function

Scott Ahlgren, Byungchan Kim

Using a family of mock modular forms constructed by Zagier, we study the coefficients of a mock modular form of weight $3/2$ on ${\mathrm{SL}}_2(\mathbb{Z})$ modulo primes $\el…