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Old 2007-12-20, 10:40   #1
devarajkandadai
 
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Default D-R zeta function

The Devaraj-Riemann zeta function is defined as follows:

Sigma(zeta(s) + n)^-s, n going from 1 to infinity.

When zeta(s) equals zero, we get the Riemann zeta function.

Q: Can this function be zero even if zeta(s) is not zero?

A.K.Devaraj
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Old 2007-12-20, 18:17   #2
ewmayer
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I like the humble naming convention best.

Last fiddled with by ewmayer on 2007-12-20 at 18:18
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Old 2007-12-20, 20:00   #3
maxal
 
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Quote:
Originally Posted by devarajkandadai View Post
The Devaraj-Riemann zeta function is defined as follows:
Sigma(zeta(s) + n)^-s, n going from 1 to infinity.
When zeta(s) equals zero, we get the Riemann zeta function.
It's nothing more than a special case of Hurwitz zeta function, namely, zeta(s,zeta(s,0)).
See http://mathworld.wolfram.com/HurwitzZetaFunction.html
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Old 2007-12-20, 20:41   #4
ewmayer
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Quote:
Originally Posted by maxal View Post
It's nothing more than a special case of Hurwitz zeta function, namely, zeta(s,zeta(s,0)).
So the "Devaraj-Riemann-Devaraj-Hurwitz-Devaraj zeta function," then?
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Old 2007-12-20, 21:37   #5
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All special cases of the jinydu function:

f(a) = b
where a is some element of a set A and b is some element of a set B



But more seriously, I don't know whether or not that function has any zeroes, other than the Riemann Zeta function's zeros. Mathematica isn't of much help because it can't evaluate the function for s\leq 1

Last fiddled with by jinydu on 2007-12-20 at 21:44
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