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...ed after [[Godfrey Harold Hardy]] and [[John Edensor Littlewood]], are two conjectures concerning the distances between zeros and the density of zeros of the [[Ri == Conjectures == ...

The conjecture states that for a polynomial ...e critical points lie within the [[convex hull]] of the roots. It follows that the critical points must be within the unit disk, since the roots are. ...

...subsets <math>B</math> and <math>C</math> of <math>\mathbb{N}</math> such that <math>A</math> contains the [[sumset]] <math>B+C</math>.<ref>{{citation|aut *[[List of conjectures by Paul Erdős]] ...

The [[theorem]] states that if <math>C</math> is the [[centralizer and normalizer|centralizer]] of an [ [[Category:Conjectures that have been proved]] ...

{{Short description|Software that produces mathematical conjectures about continued fractions}} ...{cite journal |last1=Gal Raayoni, Shahar Gottlieb, . . . |title=Generating conjectures on fundamental constants with the Ramanujan Machine |year=2021 |url=https:/ ...

...eneral [[root system]]s with the '''Macdonald constant term conjecture''', proved by [[Ivan Cherednik|Cherednik]]. The Dyson conjecture states that the Laurent polynomial ...

...the [[Riemann zeta function]] &zeta;(1/2&nbsp;+&nbsp;''it''). It is known that the function has infinitely many zeroes on this line in the complex plane: ...function conjectures|Hardy–Littlewood conjecture '''2''']]; and he proved that for any ...

...Xiv preprint]</ref> Some cases of this conjecture in dimension 2 have been proved by {{harvtxt | Dieulefait | 2004}}. ...of <math>\mathrm{Gal}(\overline{\mathbb{Q}}|\mathbb{Q})</math>. It claims that in this case, <math>\rho</math> is associated to a cuspidal newform if and ...

...of {{mvar|W}} onto the open unit disk. The '''Brennan conjecture''' states that ...onstant <math>p_0 > 3</math>.<ref name=Brennan/> Bertilsson proved in 1999 that the result holds when <math>4/3 < p < 3.422</math>, but the full result rem ...

...]]. The conjecture has been proved for dimensions 1 and 2, and it is known that the 3-dimensional version of the conjecture implies the [[Poincaré conjectu ...n, Denise|last2=Dušan|first2=Repovš|title=The Bing–Borsuk and the Busemann conjectures|journal=Mathematical Communications|date=23 December 2008|volume=13|issue=2 ...

...<math>n</math>-vertex circulant graphs, and Ádám conjectured (incorrectly) that these are the only symmetries of the circulant graphs. Toida's conjecture states that, when every member of <math>S</math> is [[relatively prime]] to <math>n</ma ...

{{For|other uniform boundedness conjectures|Uniform boundedness conjecture (disambiguation){{!}}Uniform boundedness con ...al point]]s. This is a refinement of [[Faltings's theorem]], which asserts that the set of <math>K</math>-rational points <math>C(K)</math> is necessarily ...

...many periodic points. [[Conley]] first made such a conjecture for the case that <math>M</math> is a torus. {{refn|Charles Conley, Lecture at University of ...different periodic points.{{R|GinzburgGürel2015}} On the other hand, it is proved for various types of symplectic manifolds. ...

...has a large [[subset]] whose [[centroid]] is also a lattice point. It was proved independently in the autumn of 2003 by [[Christian Reiher]], then an underg ...ists a subset <math>S_1 \subseteq S</math> with <math>n</math> points such that the centroid of all points from <math>S_1</math> is also a lattice point. ...

...try Gudkov]]) was a [[conjecture]], and is now a [[theorem]], which states that a [[Harnack's curve theorem|M-curve]] of [[parity (mathematics)|even]] degr The theorem was [[mathematical proof|proved]] by the combined works of [[Vladimir Arnold]] and [[Vladimir Abramovich Ro ...

...last=Ravenel | first=Douglas |authorlink=Douglas Ravenel| year=1984}} and proved by {{harvs|txt| last1=Devinatz | first1=Ethan S. | last2=Hopkins | first2=M ...vs|txt|last=Nishida|first= Goro|authorlink=Goro Nishida|year=1973}} showed that elements of positive degree of the [[homotopy groups of spheres]] are nilpo ...

The infinitude of <math>F(2,9)</math> was proved by computer in 1990. {{see also|Kaplansky's conjectures}} ...

...made by [[A. M. Garsia]] and [[M. Haiman]] and later [[mathematical proof|proved]] by [[M. Haiman]]. It implies [[Ian G. Macdonald|Macdonald]]'s [[Macdonald ...Hecke algebra]]s and [[Hilbert scheme]]s, which were used to prove several conjectures made by Macdonald about them. ...

{{short description|Theorem that the diffeomorphism group of the 3-sphere has the homotopy-type of O(4)}} ...its isometry group, the orthogonal group [[orthogonal group|O(4)]]. It was proved in 1983 by [[Allen Hatcher]].<ref>{{Cite journal|last=Hatcher|first=Allen E ...

...order) of [[Stark's conjecture]], when the [[place (number theory)|place]] that [[completely split|splits completely]] in the extension is finite. There a ...ath|''k''}} containing the [[Archimedean place]]s and the [[prime ideal]]s that [[Ramification theory of valuations|ramify]] in {{math|''K''/''k''}}. The ...