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# [SOLVED] Complex[2]

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Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: [SOLVED] Complex[2]   Tue Jan 05, 2010 10:38 am Back again problem

Posts : 184
Join date : 2009-09-15
Age : 32
Location : the infinite, frictionless plane of uniform density

 Subject: Re: [SOLVED] Complex[2]   Wed Jan 06, 2010 5:46 pm The function is completely determined by its values on the parallelogram with vertices w_1 and w_2, and only takes the values it takes there. Since the function is entire, it has no singularities on the parallelogram; hence it is bounded there, and hence everywhere, and by Liouville's theorem a bounded entire function is constant. Welcome back to the forum Mo!

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: Re: [SOLVED] Complex[2]   Thu Jan 07, 2010 12:14 am Almost done!Sol

Posts : 184
Join date : 2009-09-15
Age : 32
Location : the infinite, frictionless plane of uniform density

 Subject: Re: [SOLVED] Complex[2]   Thu Jan 07, 2010 10:13 am Oh yeah! For some reason I had read the problem as w_1/w_2 being in C - R. So I only took care of the first part of the problem...I should pay more attention! I thought it was a bit too easy for a Mohammad problem! It should have rung a bell. Very cool problem in retrospect though.

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: Re: [SOLVED] Complex[2]   Thu Jan 07, 2010 10:48 am When you have time please move solved problems to the other section

Euclid

Posts : 95
Join date : 2009-09-15
Age : 57
Location : Alexandria

 Subject: Re: [SOLVED] Complex[2]   Thu Feb 04, 2010 12:51 pm So, Roughly speaking, a periodical analytic entire function can not have more than one period ?Complex analysis looks to me like sculpture...

Posts : 184
Join date : 2009-09-15
Age : 32
Location : the infinite, frictionless plane of uniform density

 Subject: Re: [SOLVED] Complex[2]   Mon Feb 08, 2010 9:26 pm That is correct. A doubly periodic entire function is necessarily constant. However there are some very interesting doubly periodic meromorphic functions (the elliptic functions).