Amplification arguments for large sieve inequalities

We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular forms, where Hecke eigenvalues are thought as the analogues of the reductions of integers modulo primes.Comment: 13 pages, 1 figure; v2, version accepted for publication in Archiv der Math

Amplification arguments for large sieve inequalities

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 give