Related papers: A note on the Artin Conjecture
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We formulate an equivariant version of Greenberg's $p$-adic Artin conjecture for smoothed equivariant $p$-adic Artin $L$-functions in the context of an arbitrary one-dimensional admissible $p$-adic Lie extension of a totally real number…
In this note we collect some results on the deformation theory of toric Fano varieties.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof…
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…
We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…
We give a new proof of Chen-Lin result with Li-Zhang method.
The search for dark matter is a very wide and active field of research. Many potential hints of dark matter have appeared recently which led to a burst of theoretical activity and model building. I necessarily concentrate here only in some…
In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
We provide a proof of the Borwein Conjecture using analytic methods.
We provide new sufficient conditions under which Ryser's conjecture holds.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
In this paper we develop the theory of perverse sheaves on Artin stacks continuing the study in "The six operations for sheaves on Artin stacks I: Finite Coefficients" and "The six operations for sheaves on Artin stacks II: Adic…
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…