Characterization of ultradifferentiable test functions defined by weight matrices in terms of their Fourier Transform

Let P D2,3(n) count the number of partitions of n with designated summands in which parts are not multiples of 2 or 3. In this work, we establish congruences modulo powers of2 and 3 forP D2,3(n). For example, for eachn≥0 andα≥0P D2,3(64α+2n+54α+2)≡0(mod 24) andP D2,3(43α+3n+ 103α+2)≡0 (mod 3).