Geodesic
Additive problems with smooth integers
H. Ki1 ; H. Maier2 ; A. Sankaranarayanan3
1Department of Mathematics Yonsei University Seoul 03722, Korea and Korea Institute for Advanced Study Seoul, Korea
2Institute for Number Theory and Probability Theory University of Ulm D-89069 Ulm, Germany
3School of Mathematics TIFR Homi Bhabha Road Mumbai 400 005, India and Institute for Number Theory and Probability Theory University of Ulm D-89069 Ulm, Germany
Acta Arithmetica, Tome 175 (2016) no. 4, pp. 301-319
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the number $R_s(n)$ of representations of a positive integer $n$ $(\le X)$ in the form $n=m^2+l$ where $m$ is a natural number and $l$ is a $Y$-smooth integer. An analogous problem is also discussed for the number $R_p(n)$ of representations of $n \ (\le X)$ in the form $n = p+l$ where $p$ is a prime number and $l$ is again a $Y$-smooth number.
DOI : 10.4064/aa8205-9-2016
Keywords: study number representations positive integer kern relax form where natural number y smooth integer analogous problem discussed number representations form where prime number again y smooth number

H. Ki  1   ; H. Maier  2   ; A. Sankaranarayanan  3

1 Department of Mathematics Yonsei University Seoul 03722, Korea and Korea Institute for Advanced Study Seoul, Korea
2 Institute for Number Theory and Probability Theory University of Ulm D-89069 Ulm, Germany
3 School of Mathematics TIFR Homi Bhabha Road Mumbai 400 005, India and Institute for Number Theory and Probability Theory University of Ulm D-89069 Ulm, Germany 
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     title = {Additive problems with smooth integers},
     journal = {Acta Arithmetica},
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H. Ki; H. Maier; A. Sankaranarayanan. Additive problems with smooth integers. Acta Arithmetica, Tome 175 (2016) no. 4, pp. 301-319. doi: 10.4064/aa8205-9-2016

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