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Digital sum inequalities and approximate convexity of Takagi-type functions
- Source :
- Mathematical Inequalities and Applications 17 (2014), no. 2, 679-691
- Publication Year :
- 2012
-
Abstract
- For an integer b>=2, let s_b(n) be the sum of the digits of the integer n when written in base b, and let S_b(N) be the sum of s_b(n) over n=0,...,N-1, so that S_b(N) is the sum of all b-ary digits needed to write the numbers 0,1,...,N-1. Several inequalities are derived for S_b(N). Some of the inequalities can be interpreted as comparing the average value of s_b(n) over integer intervals of certain lengths to the average value of a beginning subinterval. Two of the main results are applied to derive a pair of "approximate convexity" inequalities for a sequence of Takagi-like functions. One of these inequalities was discovered recently via a different method by V. Lev; the other is new.<br />Comment: 15 pages
- Subjects :
- Mathematics - Number Theory
11A63 (Primary) 26A27, 26A51 (Secondary)
Subjects
Details
- Database :
- arXiv
- Journal :
- Mathematical Inequalities and Applications 17 (2014), no. 2, 679-691
- Publication Type :
- Report
- Accession number :
- edsarx.1208.2745
- Document Type :
- Working Paper