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Complete the square
How to solve quadratic equations
How to use the method of stationary phase to control oscillatory integrals
If you are calculating an integral, complex substitutions are not forbidden
Transform equation to reach a solved pattern
Use rescaling or translation to normalize parameters
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Littlewood-Paley heuristic for derivative
Littlewood-Paley heuristic
Geometric view of Hölder's inequality
Diagonal arguments
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
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