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• "short intervals"
Clear All  # Short interval asymptotics for a class of arithmetic functions

Acta Mathematica Hungarica
Authors: Mübariz Z. Garaev, Florian Luca and Werner Georg Nowak

## Summary

We provide a general asymptotic formula which permits applications to sums like \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sum_{x< n\le x+y} \big(d(n)\big)^2, \quad \sum_{x< n\le x+y} d(n^3),\quad \sum_{x< n\le x+y}\big(r(n)\big)^2, \quad \sum_{x< n\le x+y}r(n^3),$ \end{document}$where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document}$d(n)$\end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document}$r(n)$\end{document} are the usual arithmetic functions (number of divisors, sums of two squares), and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document}$y$\end{document} is small compared to~\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document}$x\$ \end{document}.

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# On the asymptotic formula for Goldbach numbers in short intervals

Studia Scientiarum Mathematicarum Hungarica
Authors: D. Bazzanella and A. Languasco

, A. and PERELLI, A., On Linnik's theorem on Goldbach numbers in short intervals and related problems, Ann. Inst. Fourier (Grenoble) 44 (1994), 307-322. MR 95g : 11097 On Linnik's theorem on Goldbach numbers in short

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# On the sum of a prime and a k-th power of prime in short intervals

Acta Mathematica Hungarica
Author: Y. C. Wang

in short intervals Sieve Methods, Exponential Sums and their Applications in Number Theory 1 – 54 10.1017/CBO9780511526091.004 . Cambridge University Press. [2

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# Exponential sums over primes in short intervals

Acta Mathematica Hungarica
Authors: A. Balog and A. Perelli
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# Distribution of the values of ω in short intervals

Acta Mathematica Hungarica
Author: G. J. Babu
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# A Note on Primes and Goldbach Numbers in Short Intervals

Acta Mathematica Hungarica
Author: A. Languasco
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# Limiting distributions of additive functions in short intervals

Acta Mathematica Hungarica
Author: K. Indlekofer
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# A note on the distribution of primes in short intervals

Acta Mathematica Hungarica
Author: J. Pintz
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# On sums of a prime and four prime squares in short intervals

Acta Mathematica Hungarica
Author: Xian-Meng Meng
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# On the maximal value of additive functions in short intervals and on some related questions

Acta Mathematica Hungarica
Authors: P. Erdős and I. Kátai
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