ON THE DISTRIBUTION OF GALOIS GROUPS

By R. Dietmann. 2010

137 citations recorded by the source corpus.

Let G be a subgroup of the symmetric group S n , and let δ G =∣ S n / G ∣ −1 where ∣ S n / G ∣ is the index of G in S n . Then there are at most O n ,ϵ ( H n −1+ δ G +ϵ ) monic integer polynomials of degree n that have Galois group G and height not exceeding H , so there are only a “few” polynomials having a “small” Galois group.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b4dd7243d5de3938f61afdf5c98cbd584deafda6

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In Discrete Mathematics and Combinatorics

1. A. Shankar
2. Manjul Bhargava
3. Xiaoheng Wang
4. Kiran S. Kedlaya
5. B. Gross

In Geometry and Topology

1. Manjul Bhargava
2. A. Shankar
3. Xiaoheng Wang
4. B. Gross
5. Bjorn Poonen
6. Melanie Matchett Wood
7. Alexei Oblomkov
8. Zhiwei Yun

In Mathematical Physics

1. A. Shankar
2. Manjul Bhargava
3. Xiaoheng Wang
4. Melanie Matchett Wood
5. B. Gross
6. Kiran S. Kedlaya
7. Bjorn Poonen
8. Alexei Oblomkov

Citations in the corpus

• Squarefree values of polynomial discriminants I (2016, background): “Following arguments of Dietmann [7], we now prove that the number of reducible monic integer polynomials of bounded height is negligible, with a power-saving error term.”