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arXiv · 1207.7178

On Additive Representation Functions

R. Balasubramanian·Sumit Giri
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Abstract

Let $\A=\{a_1<a_2<a_3.....<a_n<...\}$ be an infinite sequence of integers and let $R_2(n)=|\{(i,j):\ \ a_i+a_j=n;\ \ a_i,a_j\in \A;\ \ i\le j\}|$. We define $S_k=\s_{l=1}^k(R_2(2l)-R_2(2l+1))$. We prove that, if $L^{\infty}$ norm of $S_k^+(=\max\{S_k,0\})$ is small then $L^1$ norm of $\frac{S_k^+}{k}$ is large.

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R. Balasubramanian, Sumit Giri. 2014-05-08. On Additive Representation Functions. https://doi.org/10.1142/s1793042115500633

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