Abstract
Let λf(n) denote the nth normalized Fourier coefficient of the primitive holomorphic cusp forms of even integral weight kâ„2 for the full modular group SL(2,Z). For xâ„1, we are interested in the sums ânâ€xλf(n)â and âa2+b2â€xλf(a2+b2)â. In this paper, we are able to establish the asymptotic formulae for general cases of the power sum for every positive integer ââN. The special cases of our results improve previous results.
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