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 2007-12-20, 10:40 #1 devarajkandadai     May 2004 22×79 Posts 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
 2007-12-20, 18:17 #2 ewmayer ∂2ω=0     Sep 2002 República de California 1158010 Posts I like the humble naming convention best. Last fiddled with by ewmayer on 2007-12-20 at 18:18
2007-12-20, 20:00   #3
maxal

Feb 2005

22·32·7 Posts

Quote:
 Originally Posted by devarajkandadai 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

2007-12-20, 20:41   #4
ewmayer
2ω=0

Sep 2002
República de California

2D3C16 Posts

Quote:
 Originally Posted by maxal 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?

 2007-12-20, 21:37 #5 jinydu     Dec 2003 Hopefully Near M48 2·3·293 Posts 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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