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

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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1. de la Bretèche, R. and Tenenbaum, G., Propriétés statistiques des entiers friables. Ramanujan J. 9 2005, 13202.
2. Drappeau, S., Théorèmes de type Fouvry–Iwaniec pour les entiers friables. Compos. Math. 151 2015, 828862.
3. Fouvry, É. and Tenenbaum, G., Entiers sans grand facteur premier en progressions arithmetiques. Proc. Lond. Math. Soc. (3) 63 1991, 449494.
4. Fouvry, É. and Tenenbaum, G., Répartition statistique des entiers sans grand facteur premier dans les progressions arithmétiques. Proc. Lond. Math. Soc. (3) 72 1996, 481514.
5. Granville, A., Harper, A. and Soundararajan, K., A new proof of Halász’s Theorem, and some consequences. Preprint.
6. Granville, A. and Shao, X., Bombieri–Vinogradov for multiplicative functions, and beyond the $x^{1/2}$ -barrier. Preprint.
7. Harper, A., Bombieri–Vinogradov and Barban–Davenport–Halberstam type theorems for smooth numbers. Preprint.
8. Hildebrand, A., Integers free of large prime divisors in short intervals. Quart. J. Math. Oxford 36 1985, 5769.
9. Iwaniec, H. and Kowalski, E., Analytic Number Theory (American Mathematical Society Colloquium Publications 53 ), American Mathematical Society (Providence, RI, 2004).
10. Roth, K. F., On the large sieves of Linnik and Rényi. Mathematika 12 1965, 19.
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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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