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Over the past few decades, a vast research area in number theory is surrounded by the $p$-adic number field $\mathbb{Q}_p$ and its extensions.

My question is on different perspective.

What are the lists of some specialized journals that publishes works in $p$-adic number theory ?

I have in mind the following journals:

  • journal of number theory

  • algebra and number theory

  • acta arithmetica

  • international journal of number theory

  • Journal de Theorie des Nombres de Bordeaux

  • $p$-adic numbers, ultrametric analysis and applications

May be my ranking is not correct exactly.

All of the above journals are SCI indexed or SCI-expanded indexed except the last one. The last one seems a quite new journal, probably consisting of $14$ volumes as of year $2021$. But it seems, the last journal is emerging well over the past years looking at its Scimago impact factor (placing it in quartile $Q_2$ last year). It seems it is specially oriented for $p$-adic number field or more generally on nonarchimedian field.

As a PhD student in $p$-adic algebraic number theory, my question-

Is it worthy to publish a research paper in any one of these journals ?

Any comments please

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    $\begingroup$ I am not aware of any journals specializing in $p$-adic number theory, but any journals publishing work in number theory more generally should also take papers in that subarea. $\endgroup$
    – Wojowu
    Commented Jan 27, 2022 at 12:31
  • $\begingroup$ @Wojowu, thank you for your comment $\endgroup$
    – MAS
    Commented Jan 27, 2022 at 12:32
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    $\begingroup$ To answer the question at the end of your post: yes, it is worthwhile to publish in any of those journals. Some are much better than others, however. $\endgroup$ Commented Jan 27, 2022 at 16:40
  • $\begingroup$ @StanleyYaoXiao, thank you for your short and precise answer for my question $\endgroup$
    – MAS
    Commented Jan 27, 2022 at 17:07
  • $\begingroup$ "placing it in quartile $Q_2$ last year" -- I did not realize quartiles can be 2-adic, but maybe it's not surprising since 1/4 is a power of 2. $\endgroup$
    – KConrad
    Commented Feb 28, 2022 at 17:07

2 Answers 2

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Your question is somewhat broad, since local and p-adic fields permeate number theory and other parts of mathematics. If you want to get an idea of which journals publish articles about aspects of p-adic fields, you can look on MathSciNet. For example, there's an entire category

  • 11S Algebraic number theory: local and p-adic fields

with 14 subcategories, and there are subcategories in other sections that deal with local fields, including

  • 11D88 Diophantine equations: p-adic and power series fields
  • 11E95 Forms and linear algebraic groups: p-adic theory
  • 11F85 p-adic theory, local fields: Discontinuous groups and automorphic forms
  • 11G25 Arithmetic algebraic geometry: Varieties over finite and local fields
  • 11K41 Probabilistic theory: distribution modulo 1; metric theory of algorithms: Continuous, p-adic and abstract analogues

So for example, if you're interested in Galois cohomology associated to local fields, you could search on 11S25 in the primary and secondary fields for the year 2021. I did that and found that there are such articles published in Trans AMS, RIMS, IJNT, Proc AMS, Selecta Math, Ann Inst Fourier, J Inst Math Jussieu, Mem Soc Math Fr, Acta Math Sin, and Acta Arith. So quite a variety of journals to choose from, and that's just 2021 articles in this particular part of $p$-adic number theory.

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  • $\begingroup$ Thank you for your broad and beautiful answer $\endgroup$
    – MAS
    Commented Jan 27, 2022 at 17:09
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    $\begingroup$ You can also use zbMATH if for some reason you don't have access to MathSciNet. $\endgroup$ Commented Jan 27, 2022 at 22:51
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As a complement to Joe Silverman's answer, you can make google scholar to alert you be e-mail of new published articles (and books, preprints, etc) which contain the word "p-adic" (or any key word you like). This is really helpful if you are interested in "what's new in the p-adic world".

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  • $\begingroup$ Thank you for your nice answer $\endgroup$
    – MAS
    Commented Jan 27, 2022 at 17:11

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