Central values of zeta functions of non-Galois cubic fields

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arxiv 2107.10900 v3 pith:4GLVZAIJ submitted 2021-07-22 math.NT

Arul Shankar , Anders Södergren , Nicolas Templier This is my paper · ORCID

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keywords centralcubicfieldsfunctionsnon-galoisvalueszetadedekind

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The Dedekind zeta functions of infinitely many non-Galois cubic fields have negative central values.

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On the counting function of cubic function fields
math.NT 2025-04 conditional novelty 7.0 of 10

The number of cubic extensions of F_q(T) of discriminant q^M is C_1 q^M - C_2(M) q^(5M/6) + O(q^((2/3+epsilon)M)), with explicit constants and an unconditional omega-result for refined counts.