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Results tagged with big-list
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user 26522
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
71
votes
34
answers
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Trichotomies in mathematics
Added. Thanks to all who participated! Let me humbly apologize to those who were annoyed (quite understandably) by this thread, deeming it nothing more than an exercise in futility. If you thought the …
36
votes
What are some very important papers published in non-top journals?
Here is what naturally came to my mind, before I saw the date constraint. I will add it nonetheless, as it is a fine example of a truly significant paper published in a rather curious choice of journa …
33
votes
Proposals for polymath projects
One of Imre Ruzsa's problems [1], from 1971, asked for the slowest possible exponential growth rate of a mapping $f : \mathbb{N} \to \mathbb{Z}$ that is not a polynomial and yet shares with (integer) …
14
votes
2
answers
684
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Occurrences of D. H. Lehmer's 10-th degree polynomial
Salem numbers and Lehmer's minimum height problem are venerated not only in number theory and diophantine analysis, where they are considered naturally interesting for their own sake, but also in fiel …
14
votes
Not especially famous, long-open problems which anyone can understand
Imre Ruzsa conjectured in 1971 (Mat. Lapok 22, in Hungarian) that a congruence-preserving mapping $f : \mathbb{N} \to \mathbb{Z}$ is a polynomial as soon as the power series $A(t) := \sum_{n \in \math …
12
votes
Contest problems with connections to deeper mathematics
Sometimes, interesting clusters of questions may arise in this way.
The last problem given at the 1991 Mathematical Olympiad asked to construct an infinite bounded sequence of real numbers having $|x …
11
votes
Shortest/Most elegant proof for $L(1,\chi)\neq 0$
Here is an elementary proof, the basic idea for which is in Selberg's 1949 paper "An elementary proof of Dirichlet's theorem about primes in an arithmetic progression" (Ann. Math., vol 2, 1949, pp. 29 …
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3
votes
Examples of naturally occurring Quadratic forms or quadrics.
Binary quadratic forms arise in nature as norm forms for a quadratic field. This point of view has various consequences in number theory.
For a fixed negative discriminant (the definite case), Gauss …