3 citations · 8 across the 12 of their papers we have counts for
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Algebraic families of hyperelliptic curves violating the Hasse principle
Dong Quan Ngoc Nguyen
In , Colliot-Thélène and Poonen showed how to construct algebraic families of genus one curves violating the Hasse principle. Poonen explicitly constructed an algebraic famil…
Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields
Dong Quan Ngoc Nguyen
In this paper, we introduce a Carlitz module analogue of Mersenne primes, and prove Carlitz module analogues of several classical results concerning Mersenne primes. In contrast to…
A Carlitz module analogue of the Grunwald--Wang theorem
Dong Quan Ngoc Nguyen
The classical Grunwald--Wang theorem is an example of a local--global (or Hasse) principle stating that except in some special cases which are precisely determined, an element …
The classical umbral calculus, and the flow of a Drinfeld module
Dong Quan Ngoc Nguyen
David Goss developed a very general Fourier transform in additive harmonic analysis in the function field setting. In order to introduce the Fourier transform for continuous charac…