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- W2912294173 abstract "We consider the number π(x, y; q, a) of primes p ⩽ x such that p ≡ a (mod q) and (p − a)/q is free of prime factors greater than y. Assuming a suitable form of Elliott-Halberstam conjecture, it is proved that π(x, y; q, a) is asymptotic to ρ(log(x/q)/log y)π(x)/φ(q) on average, subject to certain ranges of y and q, where ρ is the Dickman function. Moreover, unconditional upper bounds are also obtained via sieve methods. As a typical application, we may control more effectively the number of shifted primes with large prime factors." @default.
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- W2912294173 date "2019-01-31" @default.
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- W2912294173 title "Primes in arithmetic progressions with friable indices" @default.
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- W2912294173 doi "https://doi.org/10.1007/s11425-018-9480-6" @default.
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