Algebraic Number Theory Research Paper

I am an undergraduate. I am interested in algebraic number theory.

My Background:

(1) I have read the first 5 chapters of the book Number Fields by Daniel A Marcus.

(2) I have read the first and third chapter of Koblitz's book on $p$-adic numbers.

(3) I have read the first two chapters of Janusz's Algebraic Number Fields and also some parts of the fifth chapter on class field theory.

Very often what happens with me is, I learn something properly only when I have to use it frequently while studying something more advanced. (For example, I got a better understanding of metric spaces when I took a course on functional analysis.) Keeping this in mind, I think it will be a good idea to read some papers in algebraic number theory. This will help me to consolidate whatever I have learnt so far. Also, it will help me to learn some new material.

Looking at my background, can you point me to some research papers which are accessible to undergraduates ?

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The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field.

The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory.

In a few months, JNT will have a new format with 3 sections:

Section 1 targets (possibly very long with complete proofs) high impact papers.

Section 2 is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions.

Section 3 is for Computational Number Theory.

Currently, the JNT has a large volume of submissions claiming to prove famous conjectures such as Fermat's Last Theorem, the Riemann Hypothesis, the Goldbach Problem, etc. The new JNT does not automatically referee such papers. JNT charges $2,000 or $200 a page (whichever amount is smaller) to hire a referee. If no mistakes are found, the money will be refunded and the article published in JNT.

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