User:Sintel/Zeta working page: Difference between revisions

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== Removing primes ==

An [http://mathworld.wolfram.com/EulerProduct.html Euler product] formula for the Riemann zeta function [[The Riemann zeta function and tuning/Appendix#1. Euler product expression for the zeta function|can be easily derived]]:

An [http://mathworld.wolfram.com/EulerProduct.html Euler product] formula for the Riemann zeta function [[The Riemann zeta function and tuning/Appendix#Euler product expression for the zeta function|can be easily derived]]:

:<math>\displaystyle

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In particular if we remove the prime 2, <math>\left(1 - 2^{-s}\right)\zeta(s)</math> is now dominated by 3, and the large peak values occur near [[edt|equal divisions of the tritave]] (3/1).

Along any line of constant <math>\sigma</math>, [[The Riemann zeta function and tuning/Appendix#~~1b.~~ Conversion factor for removing primes|it can be shown that]]:

Along any line of constant <math>\sigma</math>, [[The Riemann zeta function and tuning/Appendix#Conversion factor for removing primes|it can be shown that]]:

:<math>\displaystyle

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== Further information ==

For the interested reader, more information and derivations can be found in the [[The Riemann zeta function and tuning/Appendix|~~Appendix~~]].

For the interested reader, more information and derivations can be found in the [[The Riemann zeta function and tuning/Appendix|appendix]].

== Links ==

@@ Line 126: / Line 126: @@
 == Removing primes ==
-An [http://mathworld.wolfram.com/EulerProduct.html Euler product] formula for the Riemann zeta function [[The Riemann zeta function and tuning/Appendix#1. Euler product expression for the zeta function|can be easily derived]]:
+An [http://mathworld.wolfram.com/EulerProduct.html Euler product] formula for the Riemann zeta function [[The Riemann zeta function and tuning/Appendix#Euler product expression for the zeta function|can be easily derived]]:
 :<math>\displaystyle
@@ Line 137: / Line 137: @@
 In particular if we remove the prime 2, <math>\left(1 - 2^{-s}\right)\zeta(s)</math> is now dominated by 3, and the large peak values occur near [[edt|equal divisions of the tritave]] (3/1).
-Along any line of constant <math>\sigma</math>, [[The Riemann zeta function and tuning/Appendix#1b. Conversion factor for removing primes|it can be shown that]]:
+Along any line of constant <math>\sigma</math>, [[The Riemann zeta function and tuning/Appendix#Conversion factor for removing primes|it can be shown that]]:
 :<math>\displaystyle
@@ Line 164: / Line 164: @@
 == Further information ==
-For the interested reader, more information and derivations can be found in the [[The Riemann zeta function and tuning/Appendix|Appendix]].
+For the interested reader, more information and derivations can be found in the [[The Riemann zeta function and tuning/Appendix|appendix]].
 == Links ==