27,195 reputation
449108
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location Montréal, Québec
age 27
visits member for 3 years, 3 months
seen Sep 18 at 16:27

Ph.D. candidate at McGill University working in the field of number theory, under the supervision of Professor Henri Darmon.

My current interests are centered around $p$-adic modular forms, $p$-adic $L$-functions, and other topics related to the Birch and Swinnerton-Dyer conjecture.


Some fun answers of mine:

A series of rationals whose every subseries is irrational

Is every rigid field perfect?

Prove $\sum^{\infty}_{n=1} \frac{a_{n+1}-a_{n}}{a_{n}}=\infty$ for an increasing sequence $a_n$ of positive integers

The prime spectrum of a Dedekind domain

A fun integral

The same integral, solved in another way

All elements in $\mathbb{Z}/n\mathbb{Z}$ are representable as sum of a square and a cube?

Algebraic varieties in $\mathbf C^n$ have no interior points

A function with a critical point


Sep
18
awarded  Revival
Sep
1
comment Integral of inverse of square root of quartic function with real roots
Thank you @Jack!
Sep
1
answered Integral of inverse of square root of quartic function with real roots
Aug
25
comment The structure of certain quotients of a ring of algebraic integers by a principal ideal
Dear Nimda: The ring $\mathcal O_K/\mathfrak p$ is not necessarily a direct product of finite fields. If there is ramification, then $\mathcal O_K/\mathfrak p$ has nilpotent elements.
Aug
25
revised When does $V/\operatorname{ker}(\phi)\simeq\phi(V)$ imply $V\simeq\operatorname{ker}(\phi)\oplus\phi(V)$?
added 18 characters in body
Aug
25
answered When does $V/\operatorname{ker}(\phi)\simeq\phi(V)$ imply $V\simeq\operatorname{ker}(\phi)\oplus\phi(V)$?
Aug
24
comment When is the map “attaching irreducible components” an effective isomorphism?
Dear @Zhen : Thank you
Aug
24
revised When is the map “attaching irreducible components” an effective isomorphism?
added 8 characters in body; edited title
Aug
24
asked When is the map “attaching irreducible components” an effective isomorphism?
Aug
24
comment Some questions about sub-fields of the field of complex numbers
@Garabed: My pleasure!
Aug
24
comment Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
Excellent! The key is really that neat partial fraction decomposition. Any thoughts on the side question?
Aug
24
revised Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
added 2 characters in body; edited title
Aug
24
comment Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
Dear @nbubis : You are right. Sorry about that, my paper is a mess!
Aug
24
comment Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
Dear @nbubis: Thank you, I made a transcription error. It should be fixed now!
Aug
24
revised Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
added 27 characters in body; edited title
Aug
24
comment Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
Dear @Did: That is also what I suggest! But I don't want to keep all of the fun to myself. :)
Aug
24
asked Is it true that $\int_0^1 \lfloor x^{-1} \rfloor^{-1} x^n dx = \frac{1}{n+1}(\zeta(2)+\zeta(3) + \dots + \zeta(n+2) ) - 1$?
Aug
20
awarded  ring-theory
Aug
19
comment Recommended research topics for high school student
Personally, I would recommend solidifying your current knowledge before getting into research. You'll probably learn a lot more by reading and solving problems. Perhaps pick a topic, and learn all you can about it.
Aug
19
answered Some questions about sub-fields of the field of complex numbers