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P. ディリクレは，等差級数の項の中に素数が無限に存在することを証明した。この研究にあたって彼が考えた次の形の級数を (通常または特殊) ディリクレ級数という。 f(x)＝a1/1x＋a2/2x＋…＋an/nx…＝Σan/nx 。この無限級数は，実変数 x の関数であるが，x を複素変数に拡張して考察することが多い。
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