Amplification arguments for large sieve inequalities

Mathematics – Number Theory

Scientific paper

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13 pages, 1 figure; v2, version accepted for publication in Archiv der Math.

Scientific paper

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.

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