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Counting Prime $k$-tuples by LaChapelle, J. is a scholarly article available to read on EtoBox.

What is Counting Prime $k$-tuples about?

Exact summatory functions that count the number of prime $k$-tuples up to some cut-off integer are presented. Related summatory $k$-tuple analogs of the first and second Chebyshev functions are then defined. Using a gamma distribution hypothesis for prime powers, associated average summatory functions are conjectured. With exact and average summatory functions in hand, pertinent $k$-tuple zeta functions can be identified, and Perron's formula allows the formulation of $k$-tuple analogs of explicit formulae. The $k$-tuple zeta functions are then used to make some inferences about $k$-tuple primes.

Author

LaChapelle, J.

Published

2013

Language

EN