\(L^4\)-norms of Hecke newforms of large level. (English) Zbl 1336.11032
The space \(S_k (q)\) of cusp forms of weight \(k\) and trivial nebentypus for the congruence group \(\Gamma_0 (q)\) is equipped with the Petersson inner product and the corresponding \(L^p\)-norms. In this paper, the authors obtain a new upper bound for the \(L^4\)-norm of a newform in \(S_k (q)\) having a large fixed weight and a prime level \(q \to \infty\). The proof of the result is carried out by using a sharp mean value estimate for a related \(L\)-function on \(\mathrm{GL}(6)\).
Reviewer: Min Ho Lee (Cedar Falls)
MSC:
| 11F12 | Automorphic forms, one variable |
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