Related papers: On a conjecture for Rubin-Stark elements in a spec…

The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…

In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved.

The theory of Weil-Stark elements is used to develop an axiomatic approach to the formulation of refined versions of Stark's Conjecture. This gives concrete new results concerning leading terms of Artin $L$-series and arithmetic properties…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We develop a detailed arithmetic theory related to special values at arbitrary integers of the Artin $L$-series of linear characters. To do so we define canonical generalized Stark elements of arbitrary `rank' and `weight', thereby…

In this paper we construct, using Stark elements of Rubin [Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 33-62], Kolyvagin systems for certain modified Selmer structures (that are adjusted to have core rank one in the sense of [Mem. Amer.…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We prove that a refinement of Stark's Conjecture formulated by Rubin is true up to primes dividing the order of the Galois group, for finite, abelian extensions of function fields over finite fields. We also show that in the case of…

We prove a conjecture by W. Bergweiler and A. Eremenko on the traces of elements of modular group in this paper

In this article, we study the p-ordinary Iwasawa theory of the (conjectural) Rubin-Stark elements defined over abelian extensions of a CM field F and develop a rank-g Euler/Kolyvagin system machinery (where 2g is the degree of F), refining…

We provide new sufficient conditions under which Ryser's conjecture holds.

We formulate a conjecture which generalizes Darmon's "refined class number formula". We discuss relations between our conjecture and the equivariant leading term conjecture of Burns. As an application, we give another proof of the "except…

We survey recent developments on the Restriction conjecture.

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.

We prove a conjecture due to Y. Last on Jacobi matrices.

In this paper, we construct (many) Kolyvagin systems out of Stickelberger elements, utilizing ideas borrowed from our previous work on Kolyvagin systems of Rubin-Stark elements. We show how to apply this construction to prove results on the…

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.