Distribution of square-free palindromes
Abstract
An exponent of distribution 1/16 is established for square-free palindromes. The main input is an upper bound for the number of palindromes, in arithmetic progressions to large moduli, divisible by large squares. Our argument combines a simplifying reformulation with exponential-sum estimates, recent work on 6-almost-prime palindromes, and the large sieve with square moduli of Baier-Zhao.
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