Timeline for Advice: What topics to study now in analytic number Theory( And if there are video lectures( Open Online course) / Course notes available on website)
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 25, 2022 at 12:46 | vote | accept | Arnold | ||
| Apr 25, 2022 at 12:36 | history | edited | Arnold | CC BY-SA 4.0 |
deleted 524 characters in body
|
| Apr 22, 2021 at 12:39 | comment | added | Arnold | @DanielLoughran Thank you! | |
| Apr 22, 2021 at 12:02 | comment | added | Daniel Loughran | Elliptic curves are a separate branch of number theory, though of course there are overlaps. They are so ubiquitous you should definitely learn about them. | |
| Apr 22, 2021 at 7:43 | history | edited | Arnold | CC BY-SA 4.0 |
Title Edited
|
| Apr 22, 2021 at 7:40 | comment | added | Arnold | @DanielLoughran Hi! , the course here given on Elliptic curves on the website of University of copenhagen kurser.ku.dk/course/nmak16007u requires only Algebra 2 and bachelor level mathematics , So is elleptic curves part of analytic number theory or algebraic number theory ? or it is a separate branch of number theory of its own? I am a bit confused on this. Can you please shed some light on this? | |
| Apr 22, 2021 at 6:11 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
|
| Apr 22, 2021 at 6:06 | comment | added | Arnold | @TimCampion In analytic number theory I am mostly interested in multiplicative number theory ( not much in additive number theory), most interesting part were Dirichlet series Euler Products, General Dirichlet series, Behavior of Riemann Zeta Function and Dirichlet L Function,modular functions , modular forms, metric number theory. | |
| Apr 22, 2021 at 1:24 | comment | added | Tim Campion | I'm sure we can all agree on at least one thing -- we're rooting for you! I'm not a number theorist, but I have some general meta-advice: don't just talk to strangers on the internet, but seek out also people from your masters institution or others who know you personally for advice from a complementary perspective, informed by their knowledge of you personally or at least of your background. Also, what are some of your favorite theorems / topics / arguments / methods / etc. in analytic number theory? What draws you to the subject? | |
| Apr 22, 2021 at 0:37 | answer | added | Anon | timeline score: 19 | |
| S Apr 21, 2021 at 23:51 | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
corrected spelling
|
| Apr 21, 2021 at 21:33 | review | Suggested edits | |||
| S Apr 21, 2021 at 23:51 | |||||
| Apr 21, 2021 at 13:49 | comment | added | Daniel Loughran | In any case, given the books you have listed, the next natural text to look at would be "Iwaniec and Kowalski: Analytic Number Theory". This book gives a good modern graduate perspective on analytic number theory and will give you a very good idea of the kind of things out there. | |
| Apr 21, 2021 at 13:47 | comment | added | Daniel Loughran | The list which reuns gives is a list of many places where analytic number theory interacts, but it is not necessary to learn all these to do research in analytic number theory. Still, if you want to do research in pure mathematics, it is good general advice to get as wide a background as possible since a lot of mathematics is related and having a wide viewpoint can be very useful. | |
| Apr 21, 2021 at 11:58 | comment | added | Arnold | @reuns Hi, I havenot done any course on algebraic topology should I do it ? Or it's fine If I don't know algebraic topology in research in analytic number theory ? | |
| Apr 21, 2021 at 8:16 | comment | added | reuns | Analytic number theory is fun because it is connected to everything: complex analysis, real and Fourier analysis, Galois theory, algebraic geometry and abstract algebra, groups, representations, $p$-adic numbers.. For elliptic curves & modular forms you need all of these. | |
| Apr 21, 2021 at 7:42 | history | asked | Arnold | CC BY-SA 4.0 |