Jacobians for contour integrals

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I have a certain multi-dimensional contour integral
$$oint dz_1 dots oint dz_n (...) $$
and I want to perform a complex change of variables. To be concrete, I want to define new integration variables $w_k = prod_i=1^k z_i$. If these were real variables I would take the absolute value of the Jacobian. In the complex case do I take the complex modulus? (my suspicion is that this is wrong) I am also unsure of what the corresponding paths of $w_k$ in $mathbbC$ would look like.




integration complex-analysis




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    up vote
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    down vote

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    I have a certain multi-dimensional contour integral
    $$oint dz_1 dots oint dz_n (...) $$
    and I want to perform a complex change of variables. To be concrete, I want to define new integration variables $w_k = prod_i=1^k z_i$. If these were real variables I would take the absolute value of the Jacobian. In the complex case do I take the complex modulus? (my suspicion is that this is wrong) I am also unsure of what the corresponding paths of $w_k$ in $mathbbC$ would look like.




    integration complex-analysis




    share|cite|improve this question





















      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      I have a certain multi-dimensional contour integral
      $$oint dz_1 dots oint dz_n (...) $$
      and I want to perform a complex change of variables. To be concrete, I want to define new integration variables $w_k = prod_i=1^k z_i$. If these were real variables I would take the absolute value of the Jacobian. In the complex case do I take the complex modulus? (my suspicion is that this is wrong) I am also unsure of what the corresponding paths of $w_k$ in $mathbbC$ would look like.




      integration complex-analysis




      share|cite|improve this question











      I have a certain multi-dimensional contour integral
      $$oint dz_1 dots oint dz_n (...) $$
      and I want to perform a complex change of variables. To be concrete, I want to define new integration variables $w_k = prod_i=1^k z_i$. If these were real variables I would take the absolute value of the Jacobian. In the complex case do I take the complex modulus? (my suspicion is that this is wrong) I am also unsure of what the corresponding paths of $w_k$ in $mathbbC$ would look like.





      integration complex-analysis





      share|cite|improve this question










      share|cite|improve this question




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