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Let $g:\mathbb{R}\to \mathbb{R}$ be a given differentiable function of exponential decay on both sides. Now let us be given a function $f:\mathbb{R}\to \mathbb{R}$, also of exponential decay, if you ...

In this previous question it is shown that the convolution of the prime counting function $\pi$ with itself, is related to the Goldbach conjecture: $$\pi^*(n):=\sum_{k=0}^n \pi(k) \pi(n-k)$$ The ...

Consider the following formula which defines a piece-wise function which I believe corresponds to a series representation for the Dirac delta function $\delta(x)$. The parameter $f$ is the evaluation ...

The shifted convolution problem for coefficients of modular forms is well studied and many estimates were established for the shifted convolution sums of Hecke eigenvalues. So, one may ask about the ...