Questions tagged [number-theory]
A field of mathematics studying numbers, their properties and structures that arise from them.
152 questions
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What factors contributed to the renaissance of number theory in the 1970s?
I'm interested in the factors (no pun intended) that contributed to the renaissance of number theory in the 1970s. I'm looking at quite a few classic papers where I don't see equivalent work in the ...
- 141
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2
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Giza pyramids and convergents of √φ/2 — known connection?
The three main Giza pyramids have height/base ratios that are exact in royal cubits:
Pyramid
Height
Base
Ratio
Khufu (Great)
280
440
7/11
Khafre
274
411
2/3
Menkaure
125
200
5/8
These are the 4th, 5th,...
- 143
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0
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120
views
Who first proved Euclid's lemma by (strong) induction?
I mean the statement that if $p$ is prime and divides a product then it divides at least one of the factors.
5
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1
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222
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Modern context for a prize problem suggested by Gauss on "right spherical triangles whose five parts have rational sines and cosines"
On May 23, 1842, Gauss suggested - as a prize problem for the Göttingen faculty of mathematics - the following question:
To devise methods for finding any number of right-angled spherical triangles ...
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Origin of ramification/inertia in number theory?
I'm self-studying algebraic number theory, currently going over ramification. How primes split in extensions, and the nomenclature seem fine to me. In my notes I like to keep some historical ...
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0
answers
72
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When and more importantly how mathematicians came out with the word "constellation" in the number theory notion "prime constellation"?
I am impassioned by astronomy and aerospace, and I recently came across the notion in math (in number theory) of prime constellation. I haven't fully grasped this advanced notion, but it has anyhow ...
- 123
2
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1
answer
93
views
What is Lagrange's "fonctions semblables" and in which of Lagrange's papers does this term appear?
In the passage from Lemmermeyer's article David Hilbert: Die Theorie der algebraischen Zahlkörper (Jahresber. Deutsche Math. Ver. 4 (1897), 175–546) –Wie viele andere Zweige der Zahlentheorie kann man ...
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0
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69
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Iwasawa writing on Iwasawa-Tate theory
Iwasawa worked out “Tate’s thesis” (harmonic analysis on adeles and ideles to get the analytic continuation and functional equation of Hecke $L$-functions) simultaneously and independently from Tate. ...
- 6,656
2
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0
answers
104
views
Buee's objection to algebraic approaches to Pell's equation
According to the MacTutor page on Adrien Quentin Buée (https://mathshistory.st-andrews.ac.uk/Biographies/Buee/), Buée published a letter entitled "Solution to a Problem of Col Silas Titus" ...
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A topological proof of the fundamental theorem of arithmetic
I have found a paper with a topological proof of the Fundamental Theorem of Arithmetic (published in The Mathematics Student by the Indian Mathematical Society, Vol. 93, Part 3-4, 2024). You can find ...
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3
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1
answer
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The shape of j-invariant
Definition of j-invariant: $$j(\tau)=1728\frac{g_2(\tau)^3}{\Delta(\tau)}=1728\frac{g_2(\tau)^3}{g_2(\tau)^3-27g_3(\tau)^2}=1728\frac{E_4(\tau)^3}{E_4(\tau)^3-E_6(\tau)^2}$$
If you look at this ...
- 1,027
1
vote
1
answer
136
views
Where can I find original statement of Hensel lifting lemma over integers modulo prime power in Kurt Hensel's publications?
Hensel lifting lemma asserts that if a polynomial $f(x)$ with integer coefficients has a root $z$ modulo a prime power $p^n$ then with the extra assumption that $f'(z)$ does not vanish modulo $p$, ...
- 111
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139
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The development of $j$-invariant
I have always been interested in $j$-invariant. And by chance, I read the part titled Toward a History of Nineteenth-Century Invariant Theory in the book Ideas and their Reception Proceedings of the ...
- 1,027
2
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1
answer
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What is the first mention of the classical modular polynomial?
The classical modular polynomial gives a (singular) plane model for the modular curve $X_0(N)$.
I'm curious about the history of these polynomials, in particular, where and when were they first ...
- 123
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0
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Resources on the history of the well-ordering principle of $\mathbb{Z}^{+}$
Can you recommend a book or paper on the origin of what we nowadays call the well-ordering principle of $\mathbb{Z}^{+}$?
I have several doubts regarding the provenance of this important principle. ...
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