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01154nam a2200169Ia 4500 |
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10.1142-S1793042122500853 |
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220630s2022 CNT 000 0 und d |
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|a 17930421 (ISSN)
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245 |
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|a On small fractional parts of perturbed polynomials
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260 |
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|b World Scientific
|c 2022
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|a Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on the earlier work by Madritsch and Tichy. In particular, let f = P + φ where P is a polynomial of degree k and φ is a linear combination of functions of shape xc, c, 1 < c < k. We prove that for any given irrational ζ we have min 2 ≤ p ≤ Xpprime ζf(p)f,X-ρ(k)+, for P belonging to a certain class of polynomials and with ρ(k) > 0 being an explicitly given rational function in k. © 2022 World Scientific Publishing Company.
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|a Diophantine approximation
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|a exponential sums
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|a small fractional parts
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700 |
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|a Minelli, P.
|e author
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773 |
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|t International Journal of Number Theory
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856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1142/S1793042122500853
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