Vanishing conjecture for Carlitz finite zeta values
Let n>0n>0n>0 and s≥0s\geq 0s≥0 be integers. Write the base-qqq expansion of nnn as n=n0+n1q+⋯+nrqrn=n_0+n_1q+\cdots+n_rq^rn=n0+n1q+⋯+nrqr and set ℓq(n):=∑ini\ell_q(n):=\sum_i n_iℓq(n):=∑ini. For the finite zeta value of level sss and e…