Questions on number theory

  • Thread starter eljose
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let be the Dirichlet series in the form:

[tex]g(s)=\sum_{n=0}^{\infty}a(n)n^{-s} [/tex] 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

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eljose said:
let be the Dirichlet series in the form:

[tex]g(s)=\sum_{n=0}^{\infty}a(n)n^{-s} [/tex] 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

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eljose said:
[tex]g(s)=\sum_{n=0}^{\infty}a(n)n^{-s} [/tex] 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.

eljose said:
another question...where could i find Vinogradov,s work on Goldbach conjecture?..thanks.
Have you tried searching MathSciNet?
 

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