Sums of Two Squares in Short Intervals

James Maynard ()
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James Maynard: Magdalen College

A chapter in Analytic Number Theory, 2015, pp 253-273 from Springer

Abstract: Abstract We show that there are short intervals [x, x + y] containing ≫ y 1∕10 numbers expressible as the sum of two squares, which is many more than the average when y = o ( ( log x ) 5 ∕ 9 ) $$y = o((\log x)^{5/9})$$ . We obtain similar results for sums of two squares in short arithmetic progressions.

Keywords: Short Arithmetic Progressions; Small Prime Factors; Trivial Regions; Uniform Version; Independent Improvement (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_15

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DOI: 10.1007/978-3-319-22240-0_15

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