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SMOOTH-SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE $x^{1/2}$ -BARRIER

  • Sary Drappeau (a1), Andrew Granville (a2) (a3) and Xuancheng Shao (a4)
Abstract

We show that smooth-supported multiplicative functions $f$ are well distributed in arithmetic progressions $a_{1}a_{2}^{-1}\;(\text{mod}~q)$ on average over moduli $q\leqslant x^{3/5-\unicode[STIX]{x1D700}}$ with $(q,a_{1}a_{2})=1$ .

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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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