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Some thoughts on proving Fourier Inversion(Complex analysis method)
In complex analysis, we have the following well-known theorem: Theorem If , then the Fourier inversion holds, namely, given We have The proof is not easy for a beginner who just touched this theorem. As for myself, I spent a tons of time on managing the proof. So I would like […]
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Harmonic Number(2)
Our goal is to prove the following theorem by Carlo Sanna. The proof is adapted and changed slightly from his paper. Theorem. For any prime number and any , we have Lemma 1 If is prime, , and , then and Proof. . Each of the sum is by […]
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Some thoughts on proving Fourier Inversion(Complex analysis method)
In complex analysis, we have the following well-known theorem: Theorem If , then the Fourier inversion holds, namely, given We have The proof is not easy for a beginner who just touched this theorem. As for myself, I spent a tons of time on managing the proof. So I would like…