Counting non-standard binary representations

2015/09/03 by Katie Anders, Anders, Katie
Mathematics · #11A63 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11A63

paper · pdf · doi:10.48550/arxiv.1509.01285

arxiv created 2015/09/03 · openalex publication_date 2015/09/03 · arxiv updated 2015/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a finite subset of ℕ including 0 and f_A(n) be the number of ways to write n=∑_i=0^∞ε_i2ⁱ, where ε_i\inA. We consider asymptotics of the summatory function s_A(r,m) of f_A(n) from m2^r to m2^r+1-1 and show that s_A(r,m)≈ c(A,m)|A|^r for some c(A,m)∈ℚ.

Related

• Odd behavior in the coefficients of reciprocals of binary power series
• The additive problem for the number of representations as a sum of two squares
• Waring's problem with almost proportional summands
• The inverse problem for representation functions of additive bases
• The binary digits of n+t