Number theory research papers

Journal of Number Theory
  1. Journal of Combinatorics and Number Theory
  2. Number Theory
  3. [latexpage]Undergraduate Projects
  4. Number Theory Research Papers -

For the most part, I am not able to supervise students at other institutions due to lack of time. That said, exceptional situations do arise; if you think yours is one, I suggest asking your advisor at your home institution to reach out to me to clarify the situation. Matching students with problems is a complicated and difficult art.

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Some advisors take a completely hands-off approach; for instance, Hendrik Lenstra claims that he can no more suggest to his students what problems they should work on than who they should marry. In my experience, relatively few students manage this without any assistance, so I tend to take a somewhat more interventionist approach. I tend to focus on a small number of areas, which I discuss on my page of questions of interest.

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I am happy to discuss these questions to see whether one of these may lead to a suitable problem. On the other hand, I also strongly approach students to discuss with other mathematicians about possibly interesting problems. I tend to know a little bit about many topics and am willing to learn more should the situation warrant , so it is quite practical to work with me on a problem suggested by someone else.

Journal of Combinatorics and Number Theory

Indeed, several of my students so far have done exactly this. It is generally beneficial for students to have more than one project in progress at once. It is okay if not everything one is doing in graduate school ends up in the thesis, as long as it all eventually gets disseminated see below. It is the joint responsibility of advisor and student to meet often enough to ensure that adequate progress is being made.

I generally try to meet with students on a regular basis say weekly to the extent possible.

Number Theory

That said, I travel frequently , so this type of regular schedule tends to get perturbed in practice. It is not absolutely necessary for students to publish their work before completing their dissertation. At this stage in one's career, what is more important than publication is dissemination , i. Formal publication is one medium for dissemination; others include posting a preprint to one's web site or to a public server such as arXiv , e mailing a paper to appropriate mathematicians, or even simply discussing one's work with others.

The importance of dissemination cannot be understated, particularly for those planning to pursue a career in academia.

Advancement at all stages is driven largely by letters of recommendation , so it is important to keep colleagues informed of one's progress. For graduate students planning to continue to a postdoc, normally three or more letters of recommendation are needed.

[latexpage]Undergraduate Projects

One will be from the thesis advisor; ordinarily a second will be from someone else at the student's institution, and a third will be from an outside mathematician familiar with the area of reseach. It is important to develop these contacts before the time comes to ask for the letter, as we are all very busy and cannot be counted on to learn about and comment on a new topic in a couple of weeks. This all being said, I should also caution against premature dissemination.

Because mathematics is a domain in which something resembling absolute truth can be established, mathematicians have a far lower tolerance for error than other scientists. Your interest in reviewing is shared with journals or conferences when they are partnered with us.

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Number Theory Research Papers -

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No one has yet endorsed Journal of Combinatorics and Number Theory. Each works broadly in number theory and has settled conjectures and introduced new topics of study. As a case in point, Hida's theory of ordinary p-adic families, and the theories to which it gave rise constitute an area of research that is broadly studied by mathematicians around the world. His theory also provides a powerful tool for applications to Galois representations and p-adic L-functions.

Likewise, Khare and his collaborator Wintenberger proved Serre's Conjecture on modular forms, which was widely viewed as one of the most important conjectures in the field of arithmetic geometry. Since that proof, the extension of this conjecture to automorphic forms has taken hold and stimulated a great deal of research.