Is There a Relationship Between g(1-s) and g(s) in L-Dirichlet Series?

[eljose]

let be the Dirichlet series in the form:

$$g(s)=\sum_{n=0}^{\infty}a(n)n^{-s}$$ my question is if there is a relationship between g(1-s) and g(s) for any L-Dirichlet series.

another question...where could i find Vinogradov,s work on Goldbach conjecture?..thanks.

 

[matt grime]

let be the Dirichlet series in the form:

$$g(s)=\sum_{n=0}^{\infty}a(n)n^{-s}$$ my question is if there is a relationship between g(1-s) and g(s) for any L-Dirichlet series.

of course there is, though it may not be nice adn interesting.

 

[shmoe]

$$g(s)=\sum_{n=0}^{\infty}a(n)n^{-s}$$ my question is if there is a relationship between g(1-s) and g(s) for any L-Dirichlet series.

Not necessarily a nice one like the functional equations for Zeta or Dirichlet L-functions, and the question might not always even make sense. If the series for g(s) does not converge everywhere, g(1-s) won't make sense everywhere g(s) does, you have to consider if g can be extended to the entire plane.

You might want to look up what's usually called the Selberg class, it's an attempt to generalize the usual cast of L-functions.

another question...where could i find Vinogradov,s work on Goldbach conjecture?..thanks.

Have you tried searching MathSciNet?