Abstract
Let Fn be the set of cuspidal automorphic representations π of GLn over a number field with unitary central character. We prove two unconditional large sieve inequalities for the Hecke eigenvalues of π∈Fn, one on the integers and one on the primes. The second leads to the first unconditional zero density estimate for the family of L-functions L(s,π) associated to π∈Fn, which we make log-free. As an application of the zero density estimate, we prove a hybrid subconvexity bound for [Formula presented] for a density one subset of π∈Fn.
Original language | English (US) |
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Article number | 107529 |
Journal | Advances in Mathematics |
Volume | 378 |
DOIs | |
State | Published - Feb 12 2021 |
Keywords
- Automorphic representations
- L-functions
- Large sieve
- Log-free zero density estimate
- Selberg sieve
- Subconvexity
ASJC Scopus subject areas
- General Mathematics