Kummer's conjecture for cubic Gauss sums by Heath-Brown, D

“…This improves on the estimate established by Heath-Brown and Patterson [4] in demonstrating the uniform distribution of the cubic Gauss sums around the unit circle. When l = 0 it is conjectured that the above sum is asymptotically of order X-5/6, so that the upper bound is essentially best possible. …”

On finiteness conjectures for modular quaternion algebras by Bruin, N, Flynn, E, González, J, Rotger, V

“…It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a number field of bounded degree. …”

Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture by Predrag Janičić, Filip Marić, Marko Maliković

“…For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. …”
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Modified Collatz conjecture or (3a + 1) + (3b + 1)I Conjecture for Neutrosophic Numbers 〈Z ∪ I〉 by W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

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Educational leadership at 2050 : conjectures, challenges, and promises / by English, Fenwick W.

Dark energy and the refined de sitter conjecture by Prateek Agrawal, Georges Obied

“…Abstract We revisit the phenomenology of quintessence models in light of the recently refined version of the de Sitter Swampland conjecture, which includes the possibility of unstable de Sitter critical points. …”
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An analogue of Serre’s conjecture for a ring of distributions by Sasane Amol

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On the Erdős-Gyárfás Conjecture in Claw-Free Graphs by Nowbandegani Pouria Salehi, Esfandiari Hossein, Haghighi Mohammad Hassan Shirdareh, Bibak Khodakhast

Subjects: “…erdős-gyárfás conjecture…”
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Entropy bounds and the species scale distance conjecture by J. Calderón-Infante, A. Castellano, A. Herráez, L. E. Ibáñez

“…Abstract The Swampland Distance Conjecture (SDC) states that, as we move towards an infinite distance point in moduli space, a tower of states becomes exponentially light with the geodesic distance in any consistent theory of Quantum Gravity. …”
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A counter example on a Borsuk conjecture by Alejandro Cholaquidis

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The Rules that Indicate Consideration in Conjecture: An Applied Study by Ibrahem Ali Altamimi, Abd Almjed Alsalahen

Subjects: “…Rules of jurisprudence, consideration, conjecture.…”
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Counterexamples to the total vertex irregularity strength’s conjectures by Faisal Susanto, Rinovia Simanjuntak, Edy Tri Baskoro

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A conjecture on the minimal size of bound states by Ben Freivogel, Thomas Gasenzer, Arthur Hebecker, Sascha Leonhardt

“…We conjecture that, in a renormalizable effective quantum field theory where the heaviest stable particle has mass $m$, there are no bound states with radius below $1/m$ (Bound State Conjecture). …”
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Frankl's Conjecture for a subclass of semimodular lattices by Vinayak Joshi, Baloo Waphare

Subjects: “…union-closed sets conjecture…”
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Racetrack potentials and the de Sitter swampland conjectures by Jose J. Blanco-Pillado, Mikel A. Urkiola, Jeremy M. Wachter

“…The resultant potentials generically exhibit de Sitter critical points and satisfy several consistency requirements such as flux quantization, large internal volume, and weak coupling, as well as a form of the so-called Weak Gravity Conjecture. Furthermore, we compute the form of the potential around these de Sitter saddle points and comment on these results in connection to the refined and more recent version of the de Sitter Swampland Conjecture.…”
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On a conjecture for balanced symmetric Boolean functions by Cusick Thomas W., Li Yuan, Stănică Pantelimon

“…We give some results towards the conjecture that are the only nonlinear balanced elementary symmetric polynomials over GF(2), where t and are any positive integers and X(d, n) = Σ1≤i1<i2<⋯<id≤nxi1xi2 ⋯ xid.…”
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Quantum corrections and the de Sitter swampland conjecture by Keshav Dasgupta, Maxim Emelin, Evan McDonough, Radu Tatar

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Fractional Aspects of the Erdős-Faber-Lovász Conjecture by Bosica John, Tardif Claude

Subjects: “…erdős-faber-lovász conjecture…”
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Procesi’s Conjecture on the Formanek-Weingarten Function is False by Dołȩga, Maciej, Novak, Jonathan

“…In this paper, we disprove a recent monotonicity conjecture of C. Procesi on the generating function for monotone walks on the symmetric group, an object which is equivalent to the Weingarten function of the unitary group.…”
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Distance conjecture and de-Sitter quantum gravity by Hao Geng

“…Among the proposed swampland criteria the distance conjecture is the most well-motivated one from the universal behavior of string theory compactifications. …”
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