2024/09/03 by Balasubramanian, R., Dutta, Sayan
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2409.01986
We prove that if A=\a1,… ,a|A|\⊂ \1,2,… ,n\ is a Sidon set so that |A|=n1/2-L^′, then am = m⋅ n1/2 + \mathcal O( n7/8) + \mathcal O(L1/2⋅ n3/4) where L=max\0,L^′\. As an application of this, we give easy proofs of some previously derived results. We proceed on to proving that for a dense Sidon set S and for any ε >0, we have ∑a∈ S a = \frac 12 n3/2 + \mathcal O (n11/8 ) for all n≤ N but at most \mathcal Oε (N\frac 45 + ε ) exceptions.