Is Computational Number Theory Underrepresented in Online Resources?

Moni
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Computational Number Theory ?!?

I am a student of Computer Science and found many good algorithms on Number Theory while working...

But actually...honestly speaking...I don't find good sites on this particular important field...:frown:

Or even new works or research... what do you think ?
 
Physics news on Phys.org
have you tried mathforum.org they have good links to website about most of the branches of mathematics.
 


Computational Number Theory is a fascinating and important field that combines the principles of number theory with the power of computation. It involves the study of algorithms and methods for solving problems related to prime numbers, factorization, cryptography, and many other areas of number theory. As a student of Computer Science, I can understand your frustration in finding good resources on this topic. However, there are many great sites and research papers available that delve into the depths of computational number theory.

Some popular sites for computational number theory include MathWorld, Number Theory Web, and the Online Encyclopedia of Integer Sequences. These sites offer a wealth of information on different algorithms, theories, and applications of number theory in computation.

As for new works and research in this field, there is a lot of ongoing research happening in computational number theory. Many universities and research institutes have dedicated teams working on this topic, constantly developing new algorithms and methods to solve complex problems. You can also find numerous research papers published in journals and conferences that cover the latest advancements in this field.

In conclusion, computational number theory is a constantly evolving field with a lot of potential for further research. With the increasing use of technology in modern society, the importance of this field will only continue to grow. So, keep exploring and learning about this fascinating topic, and who knows, maybe you'll be the one to make groundbreaking discoveries in computational number theory!
 
##\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...
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...
When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
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