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:<math>\rho_z(a + \omega^j) \neq \rho_z(a) + \omega^j \quad (4)</math> for all <math>z \in {\bf C}, a \in R_1, j \in {\bf Z}</math>. ...

...maximum of <math>n - \uparrow\{J\}</math> over all join-irreducibles <math>J</math>; the goal is to lower bound <math>m</math> in terms of <math>n</math ...0</math> such that (weak) FUNC holds for all lattices with <math>|\mathcal{J}| \leq C|\mathcal{A}|</math>, then it holds in general. ...

:<math>C_6 := \{ \omega^j: j=0,\dots,5\}</math> ...th> to the origin, to <math>\omega^{j+1} \in C_6</math>, and <math>\omega^{j-1} \in C_6</math>. ...

:<math>D_{n,j} := \{ (x_1,\ldots,x_n) \in [3]^n: \sum_{i=1}^n x_i \neq j \ \operatorname{mod}\ 3 \}</math>. (1') ...removing the diagonal {1111,2222,3333} from <math>D_{4,j}</math> for some j=0,1,2. ...

: 1. if <math>J</math> &isin; <i>&#8464;</i> and <math>I</math> &sube; <math>J</math> then <math>I</math> &isin; <i>&#8464;</i>, and ...nd <math>|I| &lt; |J|</math> then there exists <math>x</math> &isin; <math>J</math> such that <math>I &cup; {x}</math> &isin; <i>&#8464;</i>. ...

...h>, <math>\gcd(j,2k+1)=1</math>, and <math>r = \frac{1}{2} \csc\left(\frac{j\pi}{2k+1}\right)</math> then On the other hand, for <math>k=2,j=1</math> we also know from the regular pentagon of unit sidelength that ...

...sult for all triangles in the region. More precisely, if on <math>\mathcal{J} </math> the extrema of the eigenfunctions are well away from other station For each point in <math> \mathcal{J}, </math> we would construct an approximation <math> u_J </math> to the des ...

:<math>\displaystyle \partial_t z_j(t) = 2 \sum_{k \neq j} \frac{1}{z_j(t) - z_k(t)} </math> :<math>\displaystyle \partial_t^j H_{t_0}(z) = (-1)^j k(k-1) \dots (k-2j+1) a_k (z-z_0)^{k-2j} + O( |z-z_0|^{\max(k-2j+1,0)} )</m ...

:<math> \exp( a ) = \sum_{j=0}^T \frac{a^j}{j!} + O_{\leq}( \frac{|a|^{T+1}}{(T+1)!} \exp(|a|) )</math> ...0}^T \frac{1}{j!} (B_i(\zeta,w) \varepsilon_{i,h} + w \varepsilon_{i,h}^2)^j ...

* [BI]: R. C. Baker, A. J. Irving, [http://arxiv.org/abs/1505.01815 Bounded intervals containing many * [M]: J. Maynard, [http://annals.math.princeton.edu/articles/8772 Small gaps betwee ...

| [https://arxiv.org/abs/1804.02385 J] | Contains 2 copies of J ...

| <math>t_1+\dots+t_k - t_j \leq 1</math> for all <math>j</math> <math>t_j \leq 1/\theta</math> for all <math>j</math> ...

:<math>\partial_t z_j(t) = - \sum_{k \neq j} \frac{2}{z_k(t) - z_j(t)}</math> :<math> \partial_t x_j = - \sum_{k \neq j} \frac{2 (x_k - x_j)}{(x_k-x_j)^2 + (y_k-y_j)^2} </math> ...

*Tchudakoff, N. G. Theory of the characters of number semigroups. J. Indian Math. Soc. (N.S.) 20 (1956), 11--15. MR0083515 (18,719e) *Newman, D. J. [http://www.jstor.org/stable/2036455 On the number of binary digits in a m ...

...th> and use ijk to denote the 3-set consisting of the i^th element of V_1, j^th element of V_2, and k^th element of V_3. Then 000, 001, 010, 011, 100, ...|A_{i'}\cap A_{j'}|</math> for every <math> i\ne j</math> and <math> i'\ne j'</math>. If we denote the size of the largest family of <math>k</math>-sets ...

...,x,y,z,w</math> are always understood to be in <math>G</math>, and <math>i,j,n,m</math> are always understood to be integers. ...> is conjugate to <math>zw^{-1}</math>, then <math> \|x\| \leq \frac{1}{|i+j|} ( \|w\| + \|z\| )</math>. ...

:<math>I_{t,j}(s,0) := \int_{C_j} \exp( s(1 + u - e^u) + \frac{t}{16} u^2 )\ du</math> for <math>j=1,2,3</math>, <math>C_1</math> is the diagonal line parameterised by ...

...200210/fea-granville.pdf It's As Easy As abc], Andrew Granville and Thomas J. Tucker, Notices of the AMS, November 2002. ...ition], S. Mochizuki, Arithmetic Elliptic Curves in General Position,Math. J. Okayama Univ. 52 (2010), pp. 1-28. ...

...us in <math>\overline{R}_2</math> in the form <math>z = \omega^i \eta^j, i,j \in \mathbb{Z}</math> where <math>\eta = \frac{\sqrt{33}+i\sqrt{3}}{6} = \s ...

* [http://www.cs.cmu.edu/~jcransh/papers/cranshaw_kittur.pdf J. Cranshaw and A. Kittur. The Polymath Project: Lessons from a successful on ...