Related papers: Two encounters with the p-adic Stark conjecture

The rank one Gross conjecture for Deligne-Ribet $p$-adic $L$-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue…

In this work we have carried out an approach between the nonsingular scientific cosmologies (without the initial singularity, the big bang), specially the cyclic models, and the Nietzsche's thought of the eternal recurrence. Moreover, we…

I describe the various elements of the NASA Science Mission Directorate's Astrophysics Division Research and Analysis Program and provide quantitative descriptions for factors such as proposal submission characteristics, proposal success…

In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…

Although the universe at redshifts greater than six represents only the first one billion years (<10%) of cosmic time, the dense nature of the early universe led to vigorous galaxy formation and evolution activity which we are only now…

Did time begin at a Big Bang? Will the present expansion of the universe last for a finite or infinite time? These questions sound philosophical but are becoming, now in the twenty-first century, central to the scientific study of…

We consider distinction of representations in the context of $p$-adic Galois symmetric spaces. We provide new sufficient conditions for distinction of parabolically induced representations in terms of similar conditions on the inducing data…

This doctoral dissertation presents an in-depth analysis of the first six chapters of Eddington's Fundamental Theory, sometimes referred to as his 'statistical' theory, in the context of discoveries and advancements made since its original…

This paper presents alternative ideas on the physics of time that lead to a new interpretation of cosmological redshifts. These ideas are based on the close relationship between the speed of time and entropy processes in our universe. I…

The purpose of this article is to give an overview of the series of papers [BK1], [BK2] concerning the $p$-adic Beilinson conjecture of motives associated to Hecke characters of an imaginary quadratic field $K$, for a prime $p$ which splits…

We explore Tate-type conjectures over $p$-adic fields. We study a conjecture of Raskind that predicts the surjectivity of $$ ({\rm NS}(X_{\bar{K}}) \otimes_{\mathbb{Z}}\mathbb{Q}_p)^{G_K} \longrightarrow H^2_{\rm…

In this paper we prove Vogan's conjecture on Arthur packets for general linear groups over $p$-adic fields, building on earlier work. The proof uses a special case of endoscopic lifting, adapted from the 1992 book by Adams, Barbasch and…

About 45,000 years ago, symbolic and technological complexity of human artefacts increased drastically. Computer simulations of Powell, Shennan and Thomas (2009) explained it through an increase of the population density, facilitating the…

In a 1986 paper, Smyth proposed a conjecture about which integer-linear relations were possible among Galois-conjugate algebraic numbers. We prove this conjecture. The main tools (as Smyth already anticipated) are combinatorial rather than…

In this article, we prove the $p$-adic Kazhdan-Lusztig hypothesis for $\mathrm{GL}_n(F)$. While the approach via graded affine Hecke algebras due to recent work of Solleveld leads to more general results, this article serves to completes…

This paper is around the topics I discussed in the lecture I gave at the Isaac Newton Institute in Cambridge, July 2009, in the Introductory Workshop. This paper can be read as a companion to my paper [Sa\"i di], where detailed proofs can…

A number of planet-host stars have been observed to rotate with a period equal to an integer multiple of the orbital period of their close planet. We expand this list by analyzing Kepler data of HAT-P-11 and finding a period ratio of 6:1.…

This article is the written version of the closing talk presented at the conference `A Century of Cosmology' held at San Servolo, Italy, in August 2007. I focus on the prospects of constraining fundamental physics from cosmological…

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

The three years 2001 to 2003 were the golden years of solar neutrino research. In this period, scientists solved a mystery with which they had been struggling for four decades. The solution turned out to be important for both physics and…