We give a new proof of the arithmetic large sieve inequality based on an amplification argument, and use a similar method to prove a new sieve inequality for classical holomorphic cusp forms. A sample application of the latter is also given.
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This work was completed while on sabbatical leave at the Institute for Advanced Study (Princeton, NJ). This material is based upon work supported by the National Science Foundation under agreement No. DMS-0635607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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Kowalski, E. Amplification arguments for large sieve inequalities. Arch. Math. 94, 443–457 (2010). https://doi.org/10.1007/s00013-010-0122-4
Mathematics Subject Classification (2000)
- Primary 11N35
- Large sieve inequality
- Modular form