6 papers
Iwasawa-type asymptotic formula for Taelman class groups of Drinfeld modules
Takenori Kataoka, Yoshiaki Okumura
The Taelman class groups associated to Drinfeld modules over function fields serve as an analogue of ideal class groups of number fields. In this paper, we establish an analogue of…
Torsion of rank-two -motives values in odd characteristic cyclotomic towers
Yoshiaki Okumura
For rank-two -motives defined over local fields with odd characteristic, we give an analogue of a theorem of Imai stating that abelian varieties with good reduction over -adi…
Chebyshev's bias for Fermat curves of prime degree
Yoshiaki Okumura
In this article, we prove that an asymptotic formula for the prime number race with respect to Fermat curves of prime degree is equivalent to part of the Deep Riemann Hypothesis (D…
Congruences of Galois representations attached to effective -motives over global function fields
Yoshiaki Okumura
This article investigates congruences of -adic representations arising from effective -motives defined over a global function field . We give a criterion for tw…
Parametrization of virtually -rational Drinfeld modules of rank two
Yoshiaki Okumura
For an extension of the rational function field over a finite field, we introduce the notion of virtually -rational Drinfeld modules as a function field anal…
A function field analogue of the Rasmussen-Tamagawa conjecture: The Drinfeld module case
Yoshiaki Okumura
In the arithmetic of function fields, Drinfeld modules play the role that elliptic curves play in the arithmetic of number fields. The aim of this paper is to study a non-existence…