Tagged Questions

2
votes
1answer
87 views

Relation between l-adic and l'-adic geometric monodromy

Suppose $X$ is a smooth family of algebraic varieties over the base $B:=\mathbb{P}^1\backslash\lbrace0,1,\infty\rbrace$ over $\overline{\mathbb{Q}}$; then we can form the relative …
4
votes
3answers
114 views

Sequences of evenly-distributed points in a product of intervals

Let φ be the golden ratio, (1+√5)/2. Taking the fractional parts of its integer multiples, we obtain a sequence of values in (0,1) which are in some sense "evenly distrib …
8
votes
1answer
387 views

What is a path in K-theory space?

In a comment on Tom Goodwillie's question about relating the Alexander polynomial and the Iwasawa polynomial, Minhyong Kim makes the cryptic but tantalizing statement: In brief, t …
2
votes
2answers
201 views

Spacing of zeros of zeta function on the critical line

I've been reading the paper "LARGE SPACES BETWEEN THE ZEROS OF THE RIEMANN ZETA-FUNCTION" by S. H. Saker (arXiv-0906.5458v3 [math.NT]). http://arxiv.org/abs/0906.5458. The author e …
3
votes
4answers
473 views

Why are the only numbers $m$ for which $n^{m+1}\equiv n \pmod{m}$ also the only numbers such that $\displaystyle\sum_{n=1}^{m}{n^m}\equiv 1 \bmod m$?

It can be seen here that the only numbers for which $n^{m+1}\equiv n \pmod{m}$ is true are 1, 2, 6, 42, and 1806. Through experimentation, it has been found that $\displaystyle\sum …
12
votes
0answers
244 views

Euler and the Four-Squares Theorem

There are several questions in the Euler-Goldbach correspondence that I am unable to answer. Sometimes it does not take very much: in his letter to Goldbach dated June 9th, 1750, …
0
votes
2answers
107 views

Products of linear forms in 3 variables

We say that a linear form $f=ax+by+cz$ of real coefficients is "irrational" if $a,b,c$ are linearly independent over the rationals. My question is: Are there 3 such "irrational" li …
4
votes
3answers
453 views

Probabilistic interpretation of prime number theorem

Suppose there is a function f(x) which is the "probability" that the integer x is prime. The integer x is prime with probability f(x), and then divides the larger integers with pro …
4
votes
1answer
214 views

Permutations with identical objects

Note: I tried asking this on math.stackexchange (here), but didn't really receive an answer - so I figured this might be the right place. How can I find the number of k-permutat …
4
votes
0answers
176 views

Can you get Siegel’s theorem “for free” from modularity and Mazur’s Eisenstein Ideal paper?

There is a well-known theorem of Shafarevich that given a finite set $S$ of primes the number of isomorphism classes of elliptic curves over $\Bbb Q$ with everywhere good reduction …
8
votes
1answer
284 views

Numerical evidence of Beilinson’s conjecture in local fields and function fields

The famous Beilinson's conjecture predicts a relationship between the regulator map in $K$-theory and special value of $L$-function generalizing the Dirichlet's theorem in number t …
2
votes
2answers
497 views

Why is the largest signed 32 bit integer prime?

This may be subjective, but does anyone have any insight into why this is the case? This struck me while considering that it's also the eigth Mersenne prime (2^31-1=2147483647). …
5
votes
1answer
334 views

Modular congruences related to sums of Catalan numbers

I am curious if somebody can be helpful concerning the following experimental observation: There exist two rational sequences $\alpha_0,\alpha_1,\dots$ and $\beta_0,\beta_1,\dots …
2
votes
1answer
240 views

A bound for the Manin constant

I recall that the Manin constant for a strong elliptic curve is a rational integer $c_E$ such that, for a modular parametrization $\phi: X_1(N) \to E$, one has $\phi^*(\omega_E)= 2 …
12
votes
1answer
356 views

Detecting almost-primes quickly

There are many fast algorithms (deterministic and probabilistic) for detecting primality. Are there any fast algorithms (probabilistic ones allowed) known for detecting whether a n …

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