TL;DR
This paper proves a distribution result for square-free palindromes, using advanced exponential sum estimates and sieve methods to analyze their distribution in arithmetic progressions.
Contribution
It establishes an exponent of distribution 1/16 for square-free palindromes, advancing understanding of their distribution in large moduli.
Findings
Proves an exponent of distribution 1/16 for square-free palindromes.
Uses a combination of exponential sum estimates and sieve techniques.
Relates to recent work on 6-almost-prime 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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