Displaying similar documents to “Asymptotics of the average height of 2-watermelons with a wall.”

The gcd-sum function.

Broughan, Kevin A. (2001)

Journal of Integer Sequences [electronic only]

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An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial

Hideaki Ishikawa, Kohji Matsumoto (2011)

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.

On the sum of digits of some sequences of integers

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.