Vagabond
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Member for 14 years, 6 months
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Last seen more than a month ago
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Curious about a question on zeta zeros?
A very interesting question would have been whether the Riemann zeta function have an infinite number of zeros which lies inside a vertical arithmetic progression ? ini There is a result due to putnam which says "infinite number of elements of any AP wont be zero's of the zeta function. On the non-periodicity of the zeros of the Riemann zeta-function. Amer. J. Math. 76, (1954). 97–99. jstor.org/stable/2372402?origin=crossref
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Group which "resembles" the free product of a cyclic group of order two and a cyclic group of order three, but isn't.
True. Now, How does one find a relation ? I think I have ended up asking the same question as you originally asked !!
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Group which "resembles" the free product of a cyclic group of order two and a cyclic group of order three, but isn't.
I am still wondering how to prove that the order of A.B is infinite in a neat way. There must be a way to describe the action in a simple geometric way and conclude .
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Group which "resembles" the free product of a cyclic group of order two and a cyclic group of order three, but isn't.
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structure of singular matrices whose entries have modulus one
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structure of singular matrices whose entries have modulus one
Yes, so that settles it. I realise one can pose it as a problem of linkage, if 4 rods are linked to form a quadrilateral then its not rigid so there would be a lot of solution. The question about when the matrix is further assumed to be generalized vandermonde type under the hypotheses that all entries has to be algebraic integers is what I need, I guess I should pose it as a separate question but I will try some more before that.
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structure of singular matrices whose entries have modulus one
The $N$ you took if you eliminate the first row and column we get [-1 1; 1 -1] which is singular and we have the condition that none of the sub matrices are singular. I am not sure though if that affects the rest of the construction.
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structure of singular matrices whose entries have modulus one
How do we proceed from here ? I would be eagerly waiting for the rest of the argument.
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structure of singular matrices whose entries have modulus one
When I do what you suggested I get $e^T M^{-1} e = 1$
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structure of singular matrices whose entries have modulus one
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structure of singular matrices whose entries have modulus one
Edited the question, specifying the condition that none of the minors are singular. Thanks for pointing out.
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structure of singular matrices whose entries have modulus one
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structure of singular matrices whose entries have modulus one
The requirement is none of the sub matrices are singular, I guess I have not been able to specify it clearly.
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Algebraic integers on the unit circle
I found Dirichlet's unit theorem yesterday though being absolutely unfamiliar with algebra I was rather intimidated. Can you please recommend a reference, further if you think I should read some other results which you think may be useful please do mention. Once again many thanks for your patience.
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Algebraic integers on the unit circle
@btw you guessed right about being in a fixed number field. I also have one query, this field which is a finite extension of $\mathbb Q$ when I restrict it to the unit circle I will get a multiplicative subgroup say $H$, I can now try to quotient out $H$ by the previous group generated by $\theta_i's$, what do I get ? May be one does not get anything by studying these objects and its a blind alley but then how do I know ? So I asked.