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Techniques for obtaining estimates
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How to use the method of stationary phase to control oscillatory integrals
If a parameter is generating undesirable boundary terms, try averaging over many choices of that parameter
Methods for simplifying integrals
Use Fourier expansion to eliminate nasty cutoffs
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Geometric view of Hölder's inequality
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
Lower degree by increasing dimension (or vice-versa)
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Countable but impredicative
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Higher dimensional analogues
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