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Results tagged with nt.number-theory
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user 2938
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
Bertrand's postulate
See Chandrasekharan, Analyic Number Theory, for the proof by S. S. Pillai. It is quite easy.
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2
votes
Writing down minimal Weierstrass equations
Use the PARI/GP routine ellglobalred. See here for a list of elliptic curve routines for PARI. I copy the relevant part here, from that page:
ellglobalred(E)
calculates the arithmetic conductor, the …
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2
votes
What is the history of the name "Chinese remainder theorem"?
Wikipedia says that the theorem appears in Fibonacci's Liber Abaci (1202). So that could be the first European instance where this name is used(though wikipedia does not say anything about what name w …
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4
votes
Map of Number Theory
Your question about one book for number theory is like a non-mathematician asking about one book for all mathematics. It is simply not possible. It is a growing subject in various directions. The best …
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0
votes
How to solve Diophantine equations in $F_{p}$?
This answer is tangential in the sense that it is speaking of the existence of solutions rather than counting them all. But I rather suspect that you would find this interesting.
Suppose you have a q …
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-1
votes
What is the base change in number theory?
In number theory, base change of a scheme or a variety is with respect to the underlying ring or field, is viewing the same scheme/variety over an extended ring or field, but with the "same" set of eq …
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1
vote
Christening Fermat's Little Theorem
Compared to Fermat's two squares theorem, or Fermat's four squares theorem, Fermat's Little theorem is indeed Little.
Not to mention the hard-to-prove Fermat Last Theorem, which goes under FLT; so th …
2
votes
1
vote
Accepted
How many linear terms are in the Hilbert set of H(z,t), a polynomial in 2 variables over a f...
Try Serre, Topics in Galois Theory.
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16
votes
2
answers
1k
views
Central simple algebras approach to class field theory, merits of
As noted earlier, I found reading Weil's book "Basic Number Theory" to be a harrowing experience, and I find his writing to be intrinsically hard to understand, though it is perfectly rigorous and cle …
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7
votes
1
answer
1k
views
Strongest known version of Baker's theorem
The article I have checked for Baker's theorem is Waldschmidt's. But the article and the citations therein are from the time of '88. Question:
What is the the strongest known lower bound for Baker …
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43
votes
8
answers
21k
views
Approaches to Riemann hypothesis using methods outside number theory [closed]
Background: Once an analytic number theorist remarked to me that all attempts to prove the Riemann hypothesis using number theoretic methods have failed. Since then that remark stuck in my mind.
The …
2
votes
Modular forms reference
The Anterp conference volumes, "Modular functions in one Variable - I, II, III, .... " might contain what you want. I am not sure though, as I am unable to verify it by looking into all the volumes.
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1
vote
How should I approximate real numbers by algebraic ones?
I do not know about algebraic number approximations; but the most canonical approximation to real numbers by rational numbers is the continued fraction expansion. They and their convergents (of first …
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18
votes
2
answers
3k
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References for Artin motives
I find the following description of Artin motives in Wikipedia. Since these seem to be quite related to number theory, I am interested to learn more in that context. I request the experts available in …
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