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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

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Explicit formula for elementary symmetric sum

So we have $$ e_m (n) = \sum\limits_{\matrix{ {} \cr {1\, \le \,k_{\,1} \, < \,k_{\,2} \, < \, \cdots \, < \,k_{\,m} \, \le \,n} \cr } } {\prod\limits_{1\, \le \,j\, \le \,m} {k_{\,j} } } …
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