2026/07/30 by Anji Dong, Nawapan Wattanawanichkul, Alexandru Zaharescu
paper · doi:10.1112/mtk.70120
crossref issued 2026/07/30 · crossref published 2026/07/30 · crossref published-online 2026/07/30 · crossref created 2026/07/31 · crossref deposited 2026/07/31 · crossref indexed 2026/07/31 · crossref published-print 2026/10/01
Abstract Let be the set of all cuspidal automorphic representations of , and let be a polynomial in the derivatives of ‐functions associated with representations . We establish an asymptotic formula for the number of nontrivial zeros of with . We explicitly determine the main term of this formula in terms of the dimensions, the arithmetic conductors, and the orders of differentiation of the component ‐functions. Furthermore, we show that, under certain conditions, almost all nontrivial zeros of lie near the critical line .