Determine argument of a complex function by its zeros and modulus
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Suppose we know the zeros of $a(k)$, say $ichi_n,n=1cdots N, chi_n>0$ are those zeros, and assume $a(k)$ is analytic in the upper half plane, how can we determine its argument by those zeros and its modulus?
and I wonder for $N=0$, i.e, no zeros in the upper half-plane,is it true that $$textarg a(k)=-frac1pip.v.int_-infty^inftyfracs-kds$$?
complex-analysis
asked Aug 22 at 4:57
DuFong
518414
add a comment |Â
up vote
0
down vote
favorite
Suppose we know the zeros of $a(k)$, say $ichi_n,n=1cdots N, chi_n>0$ are those zeros, and assume $a(k)$ is analytic in the upper half plane, how can we determine its argument by those zeros and its modulus?
and I wonder for $N=0$, i.e, no zeros in the upper half-plane,is it true that $$textarg a(k)=-frac1pip.v.int_-infty^inftyfracs-kds$$?
complex-analysis
asked Aug 22 at 4:57
DuFong
518414
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose we know the zeros of $a(k)$, say $ichi_n,n=1cdots N, chi_n>0$ are those zeros, and assume $a(k)$ is analytic in the upper half plane, how can we determine its argument by those zeros and its modulus?
and I wonder for $N=0$, i.e, no zeros in the upper half-plane,is it true that $$textarg a(k)=-frac1pip.v.int_-infty^inftyfracs-kds$$?
complex-analysis
asked Aug 22 at 4:57
DuFong
518414
Suppose we know the zeros of $a(k)$, say $ichi_n,n=1cdots N, chi_n>0$ are those zeros, and assume $a(k)$ is analytic in the upper half plane, how can we determine its argument by those zeros and its modulus?
and I wonder for $N=0$, i.e, no zeros in the upper half-plane,is it true that $$textarg a(k)=-frac1pip.v.int_-infty^inftyfracs-kds$$?
complex-analysis
asked Aug 22 at 4:57
DuFong
518414
asked Aug 22 at 4:57
DuFong
518414
asked Aug 22 at 4:57
DuFong
518414
asked Aug 22 at 4:57
DuFong
518414
518414
add a comment |Â
add a comment |Â
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