What question did this study set out to answer?

To characterize cyclotomic function fields with irreducible quadratic modulus over finite fields.

Cyclotomic function fields over finite fields with irreducible quadratic modulus

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Shows characterization of cyclotomic function fields in finite fields, indicating unique automorphism group structure.

To characterize cyclotomic function fields with irreducible quadratic modulus over finite fields.
Characterization of cyclotomic function fields F(Λ M) with modulus M where M is a monic irreducible polynomial of degree two.
Analysis of 𝔽 q isomorphism and rational places in the context of function fields.
Extension of previous results on automorphism groups for odd characteristic.
F(Λ M) is characterized as the only function field with q + 1 𝔽 q -rational places and a specific genus.
Computation of the full automorphism group of F(Λ M) in odd characteristic has been accomplished.

Arakelian et al. (2026) studied this question.

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View Full Paper

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Authors

Shows characterization of cyclotomic function fields in finite fields, indicating unique automorphism group structure.

To characterize cyclotomic function fields with irreducible quadratic modulus over finite fields.
Characterization of cyclotomic function fields F(Λ M) with modulus M where M is a monic irreducible polynomial of degree two.
Analysis of 𝔽 q isomorphism and rational places in the context of function fields.
Extension of previous results on automorphism groups for odd characteristic.
F(Λ M) is characterized as the only function field with q + 1 𝔽 q -rational places and a specific genus.
Computation of the full automorphism group of F(Λ M) in odd characteristic has been accomplished.

Arakelian et al. (2026) studied this question.

View Full Paper

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