Related papers: On a conjecture for Rubin-Stark elements in a spec…
In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \N$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the…
We prove that the number of partitions of an integer into at most b distinct parts of size at most n forms a unimodal sequence for n sufficiently large with respect to b. This resolves a recent conjecture of Stanley and Zanello.
In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis…
This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.
We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups. We prove Arthur's conjecture, the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group, for quasi-split special unitary groups…
We prove Rubin's conjecture on the structure of local units in the anticyclotomic $\mathbb{Z}_p$-extension of unramified quadratic extension of $\mathbb{Q}_p$ in $p=3$ case by extending Burungale-Kobayashi-Ota's work.
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
The purpose of this paper is to formulate and study a common refinement of a version of Stark's conjecture and its $p$-adic analogue, in terms of Fontaine's $p$-adic period ring and $p$-adic Hodge theory. We construct period-ring-valued…
We confirm a conjecture of Sun on the expansions of $n(m^k-1)/(m-1)$ in base $m$.
In this article several properties of the inverse along an element will be studied in the context of unitary rings. New characterizations of the existence of this inverse will be proved. Moreover, the set of all invertible elements along a…
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…
We prove a conjecture of V. V. Shokurov which in particular implies that the fibers of a resolution of a variety with divisorial log terminal singularities are rationally chain connected.
In this paper we prove the WALA conjecture.
Under certain assumptions, we prove an anticyclotomic analogue of the "weak main conjecture" \`a la Mazur and Tate for modular forms over a large class of cyclic ring class extensions.
Let $K/k$ be an abelian extension of number fields with a distinguished place of $k$ that splits totally in $K$. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in $K$, called the Stark unit,…
We prove a variant of Manin's conjecture for Campana points on wonderful compactifications of semi-simple algebraic groups of adjoint type. We use this to provide evidence for a new conjecture on the leading constant in Manin's conjecture…
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least half of its members. Although the conjecture is known to be…
Khabibullin's conjecture has three statements equivalent to each other. Recently Ruslan Sharipov has constructed a counterexample to this conjecture for one of its three statements. In this paper Sharipov's counterexample is transferred to…
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…