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On the Mertens conjecture for cusp forms
Published online by Cambridge University Press: 26 February 2010
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Before stating the main theorem, we would like to recall the basic properties of the “zeta-functions” attached to cusp forms on SL (2, ℤ). Let k be an even integer ≥ 12 and f a cusp form of weight k on SL (2, ℤ) with q-expansion We shall assume that c1 = 1, and that f is an eigenfunction of the Hecke operators. Define φ(s) as the Dirichlet series The series and the product
over the primes are equal and absolutely convergent for Re (S) > ½(k + 1).
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