### A hybrid of Darboux's method and singularity analysis in combinatorial asymptotics.

Flajolet, Philippe, Fusy, Eric, Gourdon, Xavier, Panario, Daniel, Pouyanne, Nicolas (2006)

The Electronic Journal of Combinatorics [electronic only]

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Flajolet, Philippe, Fusy, Eric, Gourdon, Xavier, Panario, Daniel, Pouyanne, Nicolas (2006)

The Electronic Journal of Combinatorics [electronic only]

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Integers

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Open Mathematics

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We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.

Hamel, A.M., King, R.C. (2011)

The Electronic Journal of Combinatorics [electronic only]

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The Electronic Journal of Combinatorics [electronic only]

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Javier Cilleruelo, Florian Luca, Juanjo Rué, Ana Zumalacárregui (2013)

Open Mathematics

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Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.

Loveless, Andrew D. (2006)

Integers

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Acta Mathematica Universitatis Comenianae. New Series

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Acta Arithmetica

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