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The Prime Index Function

Theophilus Agama ()

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 1195-1202

Abstract: Abstract In this paper we introduce the prime index function $$\iota \left( n \right) = {\left( { - 1} \right)^{\pi \left( n \right)}},$$ ι ( n ) = ( − 1 ) π ( n ) where π(n) is the prime counting function. We study some elementary properties and theories associated with the partial sums of this function given by $$\xi \left( x \right): = \sum\limits_{n \le x} {\iota \left( n \right).} $$ ξ ( x ) = ∑ n ≤ x ι ( n ) .

Keywords: Oscilloation; period; index; prime; 42C15; 41A58 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0458-9

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