Related papers: Two encounters with the p-adic Stark conjecture
This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…
We deal with the distribution of N points placed consecutively around the circle by a fixed angle of a. From the proof of Tony van Ravenstein, we propose a detailed proof of the Steinhaus conjecture whose result is the following: the N…
Theories of fundamental physics as well as cosmology must ultimately not only account for the structure and evolution of the universe and the physics of fundamental interactions, but also lead to an understanding of why this particular…
A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.
I discuss various aspects of archeoastronomy concentrating on physical artifacts (i.e., not including ethno-archeoastronomy) focusing on the period that ended about 2000 years ago. I present examples of artifacts interpreted as showing the…
Two new sufficient conditions for generalized cycles (including Hamilton and dominating cycles as special cases) in an arbitrary k-connected graph (k=1,2,...) are derived, which prove the truth of Bondy's (1980) famous conjecture for some…
We provide a detailed analysis of the problems and prospects of superstring theory c. 1986, anticipating much of the progress of the decades to follow.
Aims: Our aim is to obtain ages that are as accurate as possible for the seven nearby open clusters alpha Per, Coma Ber, IC 2602, NGC 2232, NGC 2451A, NGC 2516, and NGC 6475, each of which contains at least one magnetic Ap or Bp star.…
In 1976, Gallagher showed that the Hardy--Littlewood conjectures on prime $k$-tuples imply that the distribution of primes in log-size intervals is Poissonian. He did so by computing average values of the singular series constants over…
We review our current understanding of how the first galaxies formed at the end of the cosmic dark ages, a few 100 million years after the Big Bang. Modern large telescopes discovered galaxies at redshifts greater than seven, whereas…
The discovery of the accelerating universe in the late 1990s was a watershed moment in modern cosmology, as it indicated the presence of a fundamentally new, dominant contribution to the energy budget of the universe. Evidence for dark…
Much progress has been achieved in the age-dating of old stellar systems, and even of individual stars in the field, in the more than sixty years since the evolution of low-mass stars was first correctly described. In this paper, I provide…
This erratum remedies errors in the literature pertaining to the stable Adams conjecture. As part of the above corrections, we also identify and fix two errors in section 4 of our recent article on the subject. We thank E. Fridelander for…
In this paper, we extend the $p$-adic valuations originally obtained by Carmichael for the sequences obtained by applying M\"obius inversion to Lucas sequences to $p$-adic congruences, from which we immediately derive corresponding…
This is a talk given at the conference ``Critical Dialogues in Cosmology'' at Princeton University, June 24-- 27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and…
An anecdotal account of the author's role in the origins of lattice gauge theory, prepared for delivery on the thirtieth anniversary of the publication of "Confinement of Quarks" [Phys. Rev. D10 (1974) 2445].
In 2006, Fukaya and Kato formulated a general conjecture about $p$-adic $L$-functions for a large class of motives and derived a precise conjectural interpolation formula from the ETNC. We study this conjectural $p$-adic $L$-function in the…
The experimental study of gravity became much more active in the late 1950s, a change pronounced enough be termed the birth, or naissance, of experimental gravity physics. I present a review of developments in this subject since 1915,…
Information about the space-time evolution of colliding nuclei can be extracted correlating particles emitted from nuclear collisions. The high density of particles produced in the STAR experiment allows the measurement of non-identical…
I describe attempts to identify and understand the most isolated galaxies starting from my 1983 Leiden PhD thesis, continuing through a string of graduate theses on various aspects of this topic, and concluding with an up-to-date account of…