851 reputation
18
bio website
location Grinnell, IA
age 19
visits member for 1 year, 1 month
seen 3 hours ago

Currently enrolled in Grinnell College

Majoring in biology and math


Aug
20
comment Suppose $f$ and $g$ are meromorphic functions on $\mathbb{C}$ such that $g(z)=f(1/z)$ for $z\neq 0$. Show that $f$ is a rational function.
*Arbitrary meromorphic function is decomposable to the product of a holomorphic function without zeros and a rational function. In this case the former function is constant because of Liouville's Theorem (any every bounded entire function must be constant.)
Aug
17
comment Recommendation of analysis textbooks
You're probably right. I found many overlaps between Carothers and Komolgorov and baby Rudin, so I will not use as many texts as I planned to, and I will focus on fewer books.
Aug
17
comment Recommendation of analysis textbooks
Thanks for your recommendation. I didn't check Halmos yet, so I will definitely consider it. I always try to finish all the questions on a single book and go on to the next one and sometimes read them back to retain my memory. But I may have to change my style and follow your opinion.
Aug
16
asked Recommendation of analysis textbooks
Aug
9
revised Suppose $f$ and $g$ are meromorphic functions on $\mathbb{C}$ such that $g(z)=f(1/z)$ for $z\neq 0$. Show that $f$ is a rational function.
added 2 characters in body
Aug
9
comment Sum of two squares modulo p
You can use Legendre symbol as used in this post: math.stackexchange.com/questions/398200/…
Aug
9
revised Suppose $f$ and $g$ are meromorphic functions on $\mathbb{C}$ such that $g(z)=f(1/z)$ for $z\neq 0$. Show that $f$ is a rational function.
deleted 75 characters in body
Aug
9
revised Suppose $f$ and $g$ are meromorphic functions on $\mathbb{C}$ such that $g(z)=f(1/z)$ for $z\neq 0$. Show that $f$ is a rational function.
deleted 3 characters in body
Aug
9
answered Suppose $f$ and $g$ are meromorphic functions on $\mathbb{C}$ such that $g(z)=f(1/z)$ for $z\neq 0$. Show that $f$ is a rational function.
Aug
7
asked How to get a nice approximation of $f(N,s)=\sum_{k=0}^{N}{N \choose k}{k \choose s-k+N}$ when $N>>1$ and $|s|<<N$?
Aug
7
asked For each integer $s$, how many N-tuples with possible elements $\{0, 1, -1\}$ satisfy the condition that the sum of its elements is $s$?
Jul
14
comment Artin Algebra 2.8.3 “Does every group whose order is a power of a prime $p$ contains an element of order $p$?”
Yes, that looks more elegant.
Jul
14
accepted Artin Algebra 2.8.3 “Does every group whose order is a power of a prime $p$ contains an element of order $p$?”
Jul
14
comment Artin Algebra 2.8.3 “Does every group whose order is a power of a prime $p$ contains an element of order $p$?”
Thanks for your collection.
Jul
14
asked Artin Algebra 2.8.3 “Does every group whose order is a power of a prime $p$ contains an element of order $p$?”
Jul
12
awarded  Yearling
Jul
2
awarded  Curious
Jun
20
comment Why should $f(z)=\sqrt{z}$ be limited on $\mathbb{C}-\{z:\Re(z)\leq0\}$ to be considered as an analytic function?
Yeah, it now looks obvious to me, but I was blind for a while. I appreciate your help a lot.
Jun
20
accepted Why should $f(z)=\sqrt{z}$ be limited on $\mathbb{C}-\{z:\Re(z)\leq0\}$ to be considered as an analytic function?
Jun
20
comment Why should $f(z)=\sqrt{z}$ be limited on $\mathbb{C}-\{z:\Re(z)\leq0\}$ to be considered as an analytic function?
Thanks for your answer. I wasn't really sure that $\sqrt{z}$ is not continuous on the negative real line, but my sixth sense told me it might be not.