Weierstrass theorems and primes.

  • Thread starter Thread starter tpm
  • Start date Start date
  • Tags Tags
    Primes
tpm
Messages
67
Reaction score
0
Does 'Weirstrass theorem' allow the existence of an entire function so:

f(z)= g(z) \prod _p(1- \frac{x}{p^{k}})

so for every prime p then f(p)=0 , and k>1 and integer??

the main question is to see if a function can have all the primes as its real roots
 
Last edited:
Physics news on Phys.org
Of course a function can have the primes, and only the primes, as its only roots, although you clearly want the function to be analytic, don't you, eljose?
 

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Similar threads

I Localizing single variable quotient polynomial ring at a prime ideal
Replies
6
Views
692
I Fundamental theorem of arithmetic from Jordan-Hölder theorem
Replies
5
Views
2K
I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
Replies
48
Views
3K
I Localising a non integral domain at a prime
Replies
17
Views
1K
I Trouble understanding an online solution to an exercise in Dummit & Foote
Replies
10
Views
606
I ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?
Replies
31
Views
1K
I ##(p^k -1) \equiv X \mbox{(mod p)}## via Wilson's theorem
Replies
2
Views
1K
MHB Field extensions and Galois goup
Replies
2
Views
2K
MHB Inequality related to number of p-Sylow subgroups
Replies
2
Views
2K
MHB Prime and Maximal Ideals .... Bland -AA - Theorem 3.2.16 .... ....
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top