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Math Help - new mathematical object found

  1. #1
    Eater of Worlds
    galactus's Avatar
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    new mathematical object found

    Here is an interesting article.

    Math Gateway

    And another:

    Math Gateway
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  2. #2
    Forum Admin topsquark's Avatar
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    All right. I'll bite. What's an L-function?

    (I evidently missed this when it was posted.)

    -Dan
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by galactus View Post
    Here is an interesting article.

    Math Gateway

    And another:

    Math Gateway
    They called me crazy! but i always knew it existed! Not so crazy now, huh? Huh?!
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  4. #4
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    Quote Originally Posted by topsquark View Post
    All right. I'll bite. What's an L-function?

    (I evidently missed this when it was posted.)

    -Dan
    It is a thing in number theory.

    A Dirichlet charachter is a function \chi : \mathbb{F}_p^{\times}\mapsto \mathbb{C}^{\times} (here \mathbb{F}_p^{\times} is the non-zero elements mod p and \mathbb{C}^{\times} are the non-zero complex numbers) which satisfies \chi (ab) = \chi (a)\chi (b).

    Given a Dirichlet charachter \chi we form the Dirichlet L-series L(\chi , s)= \sum_{n=1}^{\infty}\frac{\chi (n)}{n^s} where s is complex.

    It can be proven that L(\chi , s) converges when \Re (s) > 1.
    Using analytic continuation we extend this to a meromorphic function on \mathbb{C}.
    This continued new function is called the Dirichlet L-function.
    It is related to Riemann zeta function.
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