In theoretical computer science, the log-rank conjecture states that the deterministic communication complexity of a two-party Boolean function is polynomially...

Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero...

They conjectured there is a constant C1 such that c < k exp ⁡ ( 4 3 log ⁡ k log ⁡ log ⁡ k ( 1 + log ⁡ log ⁡ log ⁡ k 2 log ⁡ log ⁡ k + C 1 log ⁡ log ⁡ k...

Do one-way functions exist? Is public-key cryptography possible? Log-rank conjecture Can integer factorization be done in polynomial time on a classical...

problems in mathematics In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even...

{\displaystyle \log \min({\textrm {rank}}(M'_{f}):M'_{f}\in \mathbb {R} ^{2^{n}\times 2^{n}},(M_{f}-M'_{f})_{\infty }\leq 1/3).} Such log rank conjectures are valuable...

Siegel, Alan (January 2000). "On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences". SIAM Journal on Computing. 30...

minimums of finite collections of polynomials. Rota's basis conjecture: for matroids of rank n {\displaystyle n} with n {\displaystyle n} disjoint bases...

field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee...

below), the rank of elliptic curves should be 1/2 on average. An even stronger conjecture is that half of all elliptic curves should have rank 0 (meaning...

In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function...

controversial argument that the continuum hypothesis is false. Woodin's Ω-conjecture asserts that if there is a proper class of Woodin cardinals (for technical...

allowing physics to form a bridge between two mathematical areas. The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine...

growth is e n {\displaystyle e^{\sqrt {n}}} . This is known as the Gap conjecture. Breuillard–Green–Tao theorem Gromov, Mikhail (1981). "Groups of polynomial...

algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of the group of units in the ring OK of algebraic integers of a number field...

k log ⁡ k ) {\displaystyle O(k{\sqrt {\log k}})} ⁠. Therefore, the graphs with bounded Hadwiger number are sparse graphs. The Hadwiger conjecture states...

embedded with smaller distortion, O ( log ⁡ n ) {\displaystyle O({\sqrt {\log n}})} . Although the GNRS conjecture remains unsolved, it has been proven...

Specifically, the Hadamard conjecture proposes that a Hadamard matrix of order 4k exists for every positive integer k. The Hadamard conjecture has also been attributed...

Mohlenkamp, along with an algorithm conjectured (but not proven) to have O ( n 2 log 2 ⁡ ( n ) ) {\textstyle O(n^{2}\log ^{2}(n))} complexity; Mohlenkamp...

it as yet unproven so is known as the sharp five exponentials conjecture. This conjecture implies both the sharp six exponentials theorem and the five...

minor may be formed by gluing together simpler pieces, and Hadwiger's conjecture relating the inability to color a graph to the existence of a large complete...

elliptic Lehmer conjecture, the curve E/K is fixed while the field of definition of the point P varies. (Lang)      h ^ ( P ) ≥ c ( K ) log ⁡ max { Norm...

line in a set of n {\displaystyle n} points in time O ( n log ⁡ n ) {\displaystyle O(n\log n)} . The Sylvester–Gallai theorem was posed as a problem by...

{R} )} should always have the property. Serre's conjecture states that a lattice in a Lie group of rank one should not have the congruence subgroup property...

conjecture is concerned with determining the rank. One conjectures that it can be arbitrarily large, even if only examples with relatively small rank...

the actor's two roles, canon demands that "Westervliet" should stand. Conjecture: Because Michael Dorn was cast in this role, it is generally assumed that...

In 1960, Claude Berge formulated another conjecture about graph coloring, the strong perfect graph conjecture, originally motivated by an information-theoretic...

log ⁡ 2 + n 1 2 log ⁡ | V 1 | + log ⁡ Γ p 1 ( n 1 2 ) − n 1 − p 1 − 1 2 E p 0 ⁡ [ log ⁡ | X | ] + 1 2 E p 0 ⁡ [ tr ⁡ ( V 1 − 1 X ) ] = n 1 p 1 2 log ⁡...

3 e , … {\displaystyle e,{}^{2}e,{}^{3}e,\dots } , given Schanuel's conjecture. It is not known whether nq is rational for any positive integer n and...

improved by any other polynomial time algorithm if the planted clique conjecture holds. amanpg - R package for Sparse PCA using the Alternating Manifold...