D-R zeta function

devarajkandadai · 2007-12-20, 10:40

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

ewmayer · 2007-12-20, 18:17

I like the humble naming convention best.

maxal · 2007-12-20, 20:00

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

ewmayer · 2007-12-20, 20:41

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?

jinydu · 2007-12-20, 21:37

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 $s\leq 1$

2007-12-20, 10:40	#1
devarajkandadai May 2004 316₁₀ 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 Califo 2²×2,939 Posts	I like the humble naming convention best. Last fiddled with by ewmayer on 2007-12-20 at 18:18

2007-12-20, 21:37	#5
jinydu Dec 2003 Hopefully Near M48 3336₈ 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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