Let , where is a finite field, let , and let be a finite extension of . Consider a Drinfeld -module over of rank . We write , where is the center of , , and . If is a prime of , we denote by the residue field at . If has good reduction at , let denote the reduction of at . In this article, in particular, when , we obtain an asymptotic formula for the number of primes of of degree for which has at most cyclic components. This result answers an old question of Serre on the cyclicity of general Drinfeld -modules. We also prove an analogue of the Titchmarsh divisor problem for Drinfeld modules.
"Cyclicity and Titchmarsh divisor problem for Drinfeld modules." Kyoto J. Math. 57 (3) 505 - 518, September 2017. https://doi.org/10.1215/21562261-2017-0004