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location Chennai, India
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visits member for 2 years, 11 months
seen 45 mins ago

Teaching at the Chennai campus of Vellore Institute of Technology, exclusively to engineering students since 2011. In an earlier job was teaching Mathematics majors; missing that atmosphere drove me to search for this type of site.


18h
answered Existence of functions on finite sets with specific propertise
Mar
16
comment Range of a trace preserving completely positive projection
Request Eckhardt to make the comment into an answer and H\'ector to accept it so that the question does not end up as showing unanswered.
Feb
20
accepted Do all algebraic number fields arise from Eisenstein polynomials?
Feb
20
comment Do all algebraic number fields arise from Eisenstein polynomials?
Thanks for a clear answer, Michael Stoll, and also to Mostafa.
Feb
20
revised Do all algebraic number fields arise from Eisenstein polynomials?
added note on abelian extension
Feb
20
asked Do all algebraic number fields arise from Eisenstein polynomials?
Feb
20
answered Irreducibility of cyclotomic polynomial over real quadratic number field
Feb
17
comment Set nor its compliment contain an uncountable closed set
The set of irrational numbers? The complement being countable satisfies. I don't know if there is an uncountable subset of irrationals that form a closed set.
Feb
12
comment Is there any Lefschetz-like principle for representations of finite groups?
Nice to get a comment from the master himself! Thanks for your explicit statement about divisibility that I did not know earlier. (Perhaps I did not study the textbooks carefully). As the divisibility proofs used the fact an algebraic integer that is rational is a usual integer I could not guess about representations in prime characteristic.
Feb
8
comment Non-principal ideals in cyclotomic fields
Here is a way: Assume the prime ideal to be principal say generated by a cyclotomic integer $\alpha$. Calculate the norm of the prime above. Then the $|N(\alpha)|$, is also norma of a suitable integer in a quadratic subfield. Choose an imaginary quadratic subfield in $Q[\zeta_{39}]$, where the norm is a positive definite quadratic form; for a binary form it should be easy to check if it assumes a specific value or not.
Feb
3
comment Is there any Lefschetz-like principle for representations of finite groups?
@Geoff Robinson: Thanks for your valuable comment connecting Eisenstein criterion. Learnt something new. I am curious about irreducible degrees not dividing the order of the group. Surprised that such a fact is not mentioned in textbooks. Can you direct me to a reference for an example of that?
Feb
3
comment Is there any Lefschetz-like principle for representations of finite groups?
Yes, I have seen that wonderful book. Remember reading from there that an irreducible complex character of degree > 1 vanishes somewhere. And the proof uses AM>GM inequality!
Feb
2
accepted Is there any Lefschetz-like principle for representations of finite groups?
Feb
2
comment Is there any Lefschetz-like principle for representations of finite groups?
@Jay Taylor: Thanks for the reference. Somehow the massive size of Curtis and Reiner made me stay away from it. I'll now definitely look up there. You have now given a clear answer. Yes, Wedderburn's structure theorem gives a way avoiding complex characters. You can make this comment an answer.
Feb
2
comment Is there any Lefschetz-like principle for representations of finite groups?
I am uncomfortable about using the property of complex conjugation. This seems to play a crucial role in the proof of Schur orthogonality relations.
Feb
2
asked Is there any Lefschetz-like principle for representations of finite groups?
Jan
27
comment Parametric solutions of Pell's equation
@StefanKohl: I was referring to rational parametrization obtained by projection for any conic; the correspondence, barring a few finite exceptions, between rational points on $P^1$ and the curve will in general be given by polynomials with rational coefficients, I am not sure now it is possible to guarantee integer coefficients.
Jan
26
comment Parametric solutions of Pell's equation
This is curve defined over Q and of degree 2. So it will be a rational curve if it has a point defined over Q. For the so called Pell's equation the hypothesis holds.
Jan
23
comment Why aren't fields called “bodies” instead?
I heard that an English translation of an early German book in algebra used "body expansion" for a field extension. I don't know if it is true.
Jan
22
comment Invariant Laurent polynomials under cyclic group action
If we take the group ring with coefficients from the ring of $p$-th cyclotomic field, then the action can be diagonalized, and invariants are readily found: then to solve your original question one has to carry out 'Galois Descent'. This is done in H W Lenstra's paper in Inventiones 1974 (in the context of Noether's problem)