3 problems

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Occurrence of type vartheta for composite radicands divisible by 5
Type- $\vartheta$ occurrence conjecture. Such composite radicands should produce cases of type $\vartheta$ in sufficiently large ranges with $D>10^3$ .
Conjecturesolvedcongruences number-fields pure-quintic-fieldsarXiv posted 2 days ago
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Infinitude of the remaining similarity classes of pure quintic fields
Infinitude conjecture. All other similarity classes are infinite.
Conjecturesolvednumber-fields pure-quintic-fieldsarXiv posted 2 days ago
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Logarithmic class-number indices as predictors of differential principal factorization types
The logarithmic-index conjecture. Computing $V_L$ , $V_M$ , and $V_N$ should save considerable CPU time in the classification algorithm, provided that rigorous proofs establish the h…
Conjecturesolvedclass-groups principal-factorization pure-quintic-fieldsarXiv posted 2 days ago

Occurrence of type vartheta for composite radicands divisible by 5