Hypothesis H and the prime number theorem for automorphic representations
نویسندگان
چکیده
For any unitary cuspidal representations πn of GLn(QA), n = 2, 3, 4, respectively, consider two automorphic representations Π and Π of GL6(QA), where Πp ∼= ∧π4,p for p 6= 2, 3 and π4,p not supercuspidal, and Π = π2 π3. First, Hypothesis H for Π and Π is proved. Then contributions from prime powers are removed from the prime number theorem for cuspidal representations π and π of GLm(QA) and GLm′(QA), respectively. The resulting prime number theorem is unconditional when m,m ≤ 4 and is under Hypothesis H otherwise.
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