Definition of weight $k$ Laplacian
$begingroup$
I just found that there are two different definitions of the weight $k$ Laplacian on the complex upper half plane. In Bump's book, he defines $Delta_{k}$ as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyfrac{partial}{partial x}
$$
but Wikipedia define it as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyleft(frac{partial}{partial x} +i frac{partial}{partial y}right)
$$
and I found some papers that use the first one, but also find paperst that use the second one, so I'm very confused now. Which one is the right one?
I think it may depend on the context, but I'm not sure.
automorphic-forms
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
$endgroup$
add a comment |
$begingroup$
I just found that there are two different definitions of the weight $k$ Laplacian on the complex upper half plane. In Bump's book, he defines $Delta_{k}$ as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyfrac{partial}{partial x}
$$
but Wikipedia define it as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyleft(frac{partial}{partial x} +i frac{partial}{partial y}right)
$$
and I found some papers that use the first one, but also find paperst that use the second one, so I'm very confused now. Which one is the right one?
I think it may depend on the context, but I'm not sure.
automorphic-forms
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
$endgroup$
add a comment |
$begingroup$
I just found that there are two different definitions of the weight $k$ Laplacian on the complex upper half plane. In Bump's book, he defines $Delta_{k}$ as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyfrac{partial}{partial x}
$$
but Wikipedia define it as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyleft(frac{partial}{partial x} +i frac{partial}{partial y}right)
$$
and I found some papers that use the first one, but also find paperst that use the second one, so I'm very confused now. Which one is the right one?
I think it may depend on the context, but I'm not sure.
automorphic-forms
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
$endgroup$
I just found that there are two different definitions of the weight $k$ Laplacian on the complex upper half plane. In Bump's book, he defines $Delta_{k}$ as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyfrac{partial}{partial x}
$$
but Wikipedia define it as
$$
Delta_{k} = -y^{2} left( frac{partial^{2}}{partial x^{2}} + frac{partial^{2}}{partial y^{2}}right) + ikyleft(frac{partial}{partial x} +i frac{partial}{partial y}right)
$$
and I found some papers that use the first one, but also find paperst that use the second one, so I'm very confused now. Which one is the right one?
I think it may depend on the context, but I'm not sure.
automorphic-forms
automorphic-forms
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
asked Jan 18 at 1:44
Seewoo LeeSeewoo Lee
6,835927
6,835927
add a comment |
add a comment |
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