Related papers: Two encounters with the p-adic Stark conjecture
An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.
In 1975, two papers were published that together sparked major new directions, conceptual, mathematical and practically applicable, in several previously disparate fields of science. In this short review, we expose key aspects of their…
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
We introduce the notion of Shintani data, which axiomatizes algebraic aspects of Shintani zeta functions. We develop the general theory of Shintani data, and show that the order of vanishing part of Gross's conjecture follows from the…
We discuss the signature of a peculiar constellation of very massive stars at a projected distance of 2-3 pc around R136a. We discuss various scenarios for its possible origin, such as independent clusters, triggered star formation,…
This paper reviews some of the important advances made over the last decade concerning theory of roAp stars.
I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Alladi-Schur polynomials.
In this thesis, we aim to develop p-adic analogs of known results for classical periods, focusing specifically on 1-motives. We establish an integration theory for 1-motives with good reductions, which generalizes the…
This article concerns two conjectures of M. P. Murthy. For Murthy's conjecture on complete intersections, the major breakthrough has still been the result proved by Mohan Kumar in 1978. In this article we improve "Mohan Kumar's bound" when…
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and…
We present a refined analysis of 15038 Kepler main sequence light curves to determine the stellar rotation periods. The initial period estimates come from an autocorrelation function, as has been done before. We then measure the duration of…
We prove the Fargues-Rapoport conjecture for p-adic period domains in the non-basic case with minuscule cocharacter. More precisely, we give a group theoretical criterion for the cases when the admissible locus and weakly admissible locus…
What is the productivity of Science? Can we measure an evolution of the production of mathematicians over history? Can we predict the waiting time till the proof of a challenging conjecture such as the P-versus-NP problem? Motivated by…
In this paper, we prove two conjectural supercongruences on the $(p-1)$th Ap\'ery number, which were recently proposed by Z.-H. Sun.
The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. The generalised Amit conjecture says that the probability of an element occurring in the image of a word map on a finite…
This article is an expanded version of the talk given by the first author at the conference "Exponential sums over finite fields and applications" (ETH, Z\"urich, November, 2010). We state some conjectures on archimedian and $p$-adic…
We formulate a global Gan-Gross-Prasad conjecture for general spin groups. That is, we formulate a conjecture on a relation between periods of certain automorphic forms on $GSpin_{n+1} \times GSpin_n$ along the diagonal subgroup $GSpin_n$…
Nov\'{a}k conjectured in 1974 that for any cyclic Steiner triple systems of order $v$ with $v\equiv 1\pmod{6}$, it is always possible to choose one block from each block orbit so that the chosen blocks are pairwise disjoint. We consider the…
Hodge Theory of $p$-adic analytic varieties was initiated by Tate in his 1967 paper on $p$-divisible groups, where he conjectured the existence of a Hodge-like decomposition for the $p$-adic \'etale cohomology of proper analytic varieties.…
We determined rotational period of practically nonrotating Ap star gamma Equ and claim $P_{\rm rot}= 97$ years. This period is about 35000 times larger than the average rotational period among stars of the same spectral class. Paper…