Thread Closed

Questions on number theory..

 
Share Thread Thread Tools
Aug27-05, 05:14 AM   #1
 

Questions on number theory..


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.
 
PhysOrg.com
PhysOrg
science news on PhysOrg.com

>> 'Whodunnit' of Irish potato famine solved
>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change
>> Curiosity Mars rover drills second rock target
Aug27-05, 07:00 AM   #2
 
Recognitions:
Homework Helper Homework Help
Science Advisor Science Advisor
Quote by eljose
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.
 
Aug28-05, 05:14 PM   #3
 
Recognitions:
Homework Helper Homework Help
Science Advisor Science Advisor
Quote by eljose
[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.

Quote by eljose
another question...where could i find Vinogradov,s work on Goldbach conjecture?..thanks.
Have you tried searching MathSciNet?
 
Thread Closed
Thread Tools


Similar Threads for: Questions on number theory..
Thread Forum Replies
Number theory questions Calculus & Beyond Homework 8
Number theory questions Calculus & Beyond Homework 9
Number theory questions Calculus & Beyond Homework 9
Questions in number theory... Linear & Abstract Algebra 3
Number theory questions Linear & Abstract Algebra 8