An induction principle for the Bombieri-Vinogradov theorem over Fq[t] and a variant of the Titchmarsh divisor problem

Dey, SampaSampaDeySavalia, AditiAditiSavalia2025-08-282025-08-282023-01-01http://arxiv.org/abs/2301.12669https://d8.irins.org/handle/IITG2025/20115Let Fq[t] be the polynomial ring over the finite field Fq. For arithmetic functions ?1,?2:Fq[t]?C, we establish that if a Bombieri-Vinogradov type equidistribution result holds for ?1 and ?2, then it also holds for their Dirichlet convolution ?1??2. As an application of this, we resolve a version of the Titchmarsh divisor problem in Fq[t]. More precisely, we obtain an asymptotic for the average behaviour of the divisor function over shifted products of two primes in Fq[t].en-USBombieri-Vinogradov theoremTitchmarsh divisor problemPolynomial ringDirichlet convolutionFinite fieldAn induction principle for the Bombieri-Vinogradov theorem over Fq[t] and a variant of the Titchmarsh divisor probleme-Printe-Print123456789/555