<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      Questions tagged [nt.number-theory]

      Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

      -4
      votes
      1answer
      43 views

      How to solve a Diophantine equation in six variables? [on hold]

      Find all the integer solutions $a, b, c, d, e, f$ satisfying the equation $a^2b^3 + c^2d^3 = e^2f^3$. Note that if we prove that there are no such solutions with the condition $\text{gcd}(ab, cd, ef) ...
      4
      votes
      1answer
      196 views

      Applications of the idea of deformation in algebraic geometry and other areas?

      The idea of proving something by deforming the general case to some special cases is very powerful. For example, one can prove certain equalities by regarding both sides as functions/sheaves, and show ...
      2
      votes
      1answer
      249 views

      Are there infinitely many prime p, such that p=1296k^2+36k+7? [on hold]

      I encountered a number theory problem when doing my research: 1.I want to know whether or not there are infinitely many primes $p$ satistying $gcd(\frac{p-1}{6},6)=1$, such that $6$ is a cubic ...
      1
      vote
      0answers
      51 views

      theta function with a low bound in the sum

      I encounter a sum similar to the Jacobi Theta function except there is a lower bound $-J$ with $J\geq 0$: \begin{equation} f(q,x)=\sum_{n=-J}^\infty q^{n^2}x^n. \end{equation} My question is whether ...
      4
      votes
      1answer
      552 views

      Partial sums of primes

      $2+3+5+7+11+13...$ is clearly the sum of the primes. Now I consider partial sums such: $2+3+5+7+11=28$ which is divisible by $7$ My question is: are there infinitely many partial sums such that: $...
      -3
      votes
      0answers
      164 views

      Fermat's last theorem related question [on hold]

      From the $ABC$ Conjecture it is possible to derive the next result $\bf{Proposition}$ $1.$ Consider some large enough different primes $p, q$, then the equation $A^pB^q + C^pD^q = E^pF^q$ has no ...
      0
      votes
      1answer
      112 views

      Calculating the number of solutions of integer linear equations

      Let $N$ be a natural number. Consider the following set of matrices whose entries are non-negative integers: $$X_N:=\left\{(c_{ij})_{i,j=1}^4\in M_4(\mathbb{Z}_{\geq 0})\bigg| \sum_j c_{1j} = \sum_i ...
      2
      votes
      0answers
      81 views

      Rationality of motivic zeta function for smooth Fano varieties

      Assume the base field is complex number, and the coefficent is the Grothendieck ring of varieties (or it's localization at $[\mathbb L]$). We know the motivic zeta function for smooth projective ...
      2
      votes
      0answers
      54 views

      How to express the cuspidal form in terms of Poincare series?

      Sorry to disturb. I recently read Blomer's paper. There is a blur which needs the expert's help here. Blomer's paper says "For any cusp form $f$ of integral weight $k$, level $N$, $f$ can be written ...
      0
      votes
      0answers
      107 views

      How many solutions to $p_i|a_{i,1} p_1 + \dotsc + a_{i,n} p_n$?

      Consider a system of $n$ divisibility conditions on $n$ prime variables: $$p_i|a_{i,1} p_1 + \dotsc + a_{i,n} p_n,\;\;\;\;\;1\leq i\leq n,$$ where $a_{i,j}$ are bounded integers. How many solutions ...
      1
      vote
      1answer
      104 views

      Power series rings and the formal generic fibre

      Let $S = K[[S_1,\ldots,S_n]]$ and consider $d$ elements \begin{equation*} f_1,\ldots,f_d \in S[[X_1,\ldots,X_d]] \end{equation*} and the prime ideal ${\frak P} \colon\!= (f_1,\ldots,f_d)$ generated ...
      2
      votes
      0answers
      86 views

      Satake correspondence for groups over finite field

      I asked the same question in MSE, but I didn't get any answer. So I decided to post it here, too. In Langlands' program, Satake correspondence gives a correspondence between unramified ...
      3
      votes
      0answers
      51 views

      Supremum of certain modified zeta functions at 1

      Let $D$ be an integer number and let $\chi$ be the Dirichlet character defined by $$\chi(m) = 0 \text{ if $m$ even, } \chi(m) = (D/m) \text{ if $m$ odd,}$$ where $(D/m)$ denotes the Jacobi symbol. ...
      5
      votes
      1answer
      113 views

      Modified Pascal's triangle

      I posted this question to Mathematics Stack Exchange but got no answers. I hope that this question is advanced enough for this forum: In Pascal's triangle, each number is the sum of the two numbers ...
      0
      votes
      0answers
      82 views

      Upper bounds for $|\theta(x)-x|$ assuming Riemann Hypothesis

      What are the best currently known upper bounds for $|\theta(x)-x|$ assuming the Riemann Hypothesis, where $\theta(x)$ is the Chebyshev theta, and can someone provide the reference for this (not ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>