An induction principle for the Bombieri-Vinogradov theorem over \(\mathbb{F}_q [t]\) and a variant of the Ttchmarsh divisor problem. (English) Zbl 1521.11058
Y. Motohashi [Proc. Japan Acad. 52, 273–275 (1976; Zbl 0355.10035)] proved that if two arithmetic functions \(f,g : \mathbb{N} \rightarrow \mathbb{C}\) satisfy a Bombieri-Vinogradov type distribution property together with certain other natural conditions, then so does their convolution \(f \ast g\). The authors establish an analogous result for polynomial rings \(\mathbb{F}_q[t]\) over the finite field \(\mathbb{F}_q\). Based on this result, they establish an asymptotic formula for the average of the divisor function over shifted products of two primes in \(\mathbb{F}_q[t]\).
Reviewer: Stephan Baier (Hāoṛā)
MSC:
| 11N37 | Asymptotic results on arithmetic functions |
| 11N13 | Primes in congruence classes |
| 11N35 | Sieves |
| 11L40 | Estimates on character sums |
| 11N36 | Applications of sieve methods |
Keywords:
finite fields; function fields; divisor function; Bombieri-Vinogradov theorem; large sieve inequality; Titchmarsh divisor problemCitations:
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