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Is there a nice theorem or toy problem that demonstrates the usefulness of invariant theory to tackle a number theoretic problem? I'm looking for some accessible insight into the motivation (for a number theorist) in studying Invariant theory.


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What's a "vector" invariant? It's mentioned in the title of your question but not explained in the body. –  Christian Blatter Sep 2 '12 at 19:28
How about Manjul Bhargava's work on the Birch--Swinnerton-Dyer conjecture? –  David Loeffler Sep 2 '12 at 19:58

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