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Displaying similar documents to “Slightly improved sum-product estimates in fields of prime order”

On the class numbers of real cyclotomic fields of conductor pq

Eleni Agathocleous (2014)

Acta Arithmetica

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The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields...

Greatest prime divisors of polynomial values over function fields

Alexei Entin (2014)

Acta Arithmetica

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For a function field K and fixed polynomial F ∈ K[x] and varying f ∈ F (under certain restrictions) we give a lower bound for the degree of the greatest prime divisor of F(f) in terms of the height of f, establishing a strong result for the function field analogue of a classical problem in number theory.