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<-------- Over there, you'll find my website.


Jul
1
reviewed Close What conditions imply that a function over $\mathbb{Z}$ is a polynomial?
Jul
1
reviewed Close Automorphism group of the gamma factor of a certain type of L-function
Jun
28
awarded  Nice Answer
Jun
28
reviewed Close How to write an abstract for a math paper?
Jun
27
comment What is known about order of torsion of jacobian of hyperelliptic curve over finite field?
Just a comment prompted by the other comments. There is no need for the Weil conjectures or Lang-Weil. By the class number formula $\# J(F_q) = \prod (1-\alpha_i)$ where the $\alpha_i$ are the zeros of the zeta function of the curve and have absolute value $\sqrt q$ by Weil.
Jun
21
comment The significance of the Parvaresh-Vardy curve
Could you make the question self-contained? In particular, what are $E,f,Q$, how do you define the curve?
Jun
16
awarded  Good Answer
Jun
15
awarded  Enlightened
Jun
15
awarded  Nice Answer
Jun
15
awarded  Nice Answer
Jun
15
answered Can we find two positive integers $n$ and $m$ ($n,m>1$) such that $n^\pi = m$?
Jun
14
comment Can we find two positive integers $n$ and $m$ ($n,m>1$) such that $n^\pi = m$?
Apply Schanuel to $2\pi i, \log n, \log m$. The last two numbers are linearly independent over $\mathbb{Q}$ because of your hypothesis and the fact that $\pi$ is irrational. Then all three numbers are linearly independent over $\mathbb{Q}$ since $2\pi i$ is not real. Finally, the exponentials of all three numbers are rational, so Schanuel implies that the three numbers are algebraically independent over $\mathbb{Q}$ which is stronger than what you want.
Jun
14
comment Can we find two positive integers $n$ and $m$ ($n,m>1$) such that $n^\pi = m$?
This follows from Schanuel's conjecture but it's probably hard to prove unconditionally.
May
22
answered Is g( ) rational if it looks that way on a large rational subset?
May
22
comment Is g( ) rational if it looks that way on a large rational subset?
@DavidHolmes The question makes sense. Maybe it's clearer to ask whether, given the conditions, there is a rational function $g_1$ satisfying the same hypotheses as $g$.
Apr
29
answered Examples of quotients by infinitesimal group schemes
Apr
20
comment Parity-check matrix for code with variable block size and minimum distance
The main conjecture of MDS codes states that there is no code with length + 1 = dimension + min. distance (writing out since your notation is nonstandard) for length > q+2. You want to relax this to length=dim. + distance but want length up to $q^2$. I doubt it can be done.
Apr
12
awarded  Good Question
Apr
9
revised What is the best known lower bound for: $\max_{2\leq i\leq p-1}(ord_n(i)) $?
added 4 characters in body
Apr
9
answered What is the best known lower bound for: $\max_{2\leq i\leq p-1}(ord_n(i)) $?