Nilmoni Karak

Sharp lower bounds for shifted moments of Dedekind zeta functions

Let $K_1,\cdots,K_r$ be fixed number fields, and let $L$ be the compositum of their Galois closures. Assuming GRH for $\zeta_L$, we prove a sharp lower bound for products of shifted Dedekind zeta functions on the critical line, for arbitrary fixed positive real exponents and uniformly for shifts of size at most $T/2$....