Related papers: Much ado about Zero
We present a streamlined proof (and some refinements) of a characterization (due to F. Carlson and G. Bourion, and also to P. Erd\"os and H. Fried) of the so called Szeg\"o's power series. This characterization is then applied to readily…
The existence of non trivial zeros off the critical line for a function obtained by analytic continuation of a particular Dirichlet series is studied. Contrary to what has been presumed for a long time, we prove that such zeros cannot…
The purpose of this book is two fold. (1) To give a systematic account of classical "zero theory" as developed by Jensen, P\'olya, Titchmarsh, Cartwright, Levinson and others. (2) To set forth developments of a more recent nature with a…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
This article gives a brief survey of the theory and applications of anomalies.
We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.
This is an elementary review of the history and physics of neutrinos. The story of the discovery of neutrino mass through neutrino oscillations is described in some detail. Experiments on solar neutrinos and atmospheric neutrinos played an…
I briefly review the main ideas and challenges involved in the computation of the observed baryonic asymmetry of the Universe.
We prove a curious identity for the Bernoulli numbers.
The article focuses on the problems of prime gaps and zero spacings. Possible solutions of several related problems such as the greatest lower bound, the least upper bound of the zero spacings, and the least upper bound of the prime gaps…
This is an attempt to illustrate the glorious history of logical foundations and to discuss the uncertain future.
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
We introduce a novel collection of uniqueness problems, with related sampling and interpolation issues. We call them deep zero problems, as they are concerned with local properties at a small number of given points.
The (partially) ordered set of the non-trivial zeros of the zeta function with positive imaginary parts is considered. The order is the coordinatewise order inherited from $\mathbb{C}$. Some interesting properties regarding the minimal…
This is an introductory article to the theory of multiple gaps.
The long story of the oscillatory approach to the initial cosmological singularity and its more recent incarnation in multidimensional universe models is told.
Our number system is a magnificent tool. But it is far from perfect. Can it be improved? In this paper some possibilities are discussed, including the use of a different base or directed (negative as well as positive) numerals. We also put…
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by…