1,721,883 research outputs found
Book Review: Mohan K. Tikku, After the Fall: Sri Lanka in Victory and War
No full text Mohan K. Tikku, After the Fall: Sri Lanka in Victory and War. New Delhi: OUP, 2016, pp. 308, Price ₹650. </jats:p
A number theoretic estimate of Davenport from a functional analytic viewpoint
No full textWe consider the problem of the identification of real continuos functions defined on [0,1], by means of the sums of the values f(a/n) with a=1,...,n (this is Fine's problem). This is not possible, in general (Besicovitch example), but we prove that it may be the case under auxiliary condition. We also study the behavior of a well known exceptional function
Extremal values of \Delta(x,N)=\sum\sb {n
No full textThe function Delta(x,N) (which measures the discrepancy of Euler's phi function) as defined in the title is closely associated to several problems in the upper bound sieve.It is also known via a classical theorem of Franel that certain conjectured bounds involving certain averages of Delta(x,N) are equivalent to the Riemann Hypothesis.We improve the unconditional bounds which have been hitherto obtained for Delta(N) and show that these are close to being optimal
Links between \Delta(x,N)=\sum\Sb n\leq xN\\(n,N)=1\endSb 1-x\phi(N) and character sums.
No full textWe express Delta(x,N), as defined in the title, for x=a/q and q prime in terms of values of characters modulo q.
Using this, we show that the universal lower bound for Delta(N)= sup|Delta(x,N)| can, in general, be substantially improved when N is composed of primes lying in a fixed residue class modulo q.
We also prove a corresponding improvement when N is the product of the first s primes for infinitely many natural numbers s
Vector resonances in weak-boson-fusion at future pp colliders
Get PDFWe present a first estimate of the reach of future pp colliders, the 14 TeV LHC and a futuristic 100 TeV pp collider, on a vector resonance, specifically a W′, produced via weak-boson-fusion, and decaying dominantly into tb. The analysis is motivated by Composite Higgs, Randall-Sundrum and Little Higgs scenarios, which predict the existence of vector resonances with a large coupling to W and Z longitudinal bosons. In particular, in composite Higgs models with partial compositeness, the standard Drell-Yan production channel is suppressed at large coupling while the weak-boson-fusion is enhanced and could thus provide a unique opportunity to directly test the large coupling regime of the theory. We outline a search strategy for the W′ in the weak-boson-fusion channel and present the reach of future colliders on the W′ mass vs coupling parameter space
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
An extension of a result of lehmer on numbers coprime to n
No full textIn this paper we study the problem of the discrepancy of Euler's phi-function and, extending a result of Lehmer, we give new examples in which the order of the discrepancy is maximum. Lehmer proved his result only for numbers N which are composed of primes congruent to -1 mod q, with q>1. We extend this result so that the assumption regarding the residue classes moq q of the primes p composing N is far weaker
Smooth numbers and the norms of arithmetic Dirichlet convolutions
No full textIn this paper we consider the problem of exactly evaluating the p-norm of a linear operator linked with arithmetic Dirichlet convolutions. We prove that a simply derived upper bound for this norm is actually attained for several different classes of arithmetic functions including completely multiplicative functions, but not for certain multiplicative functions. Our proof depends fundamentally on the asymptotic distribution properties of smooth numbers
Calculating a determinant associated with multiplicative functions.
No full textLet h be a complex valued multiplicative function.
For any natural N, we compute the value DN:= det (h((i,j))/ij) with i|N,j|N, where (i,j) denotes the greatest common divisor of i and j, which appear in increasing order in rows and columns.
We prove that the 1/t(N) root of DN (where t(N) is the number of divisors of N) is a multiplicative function of N.
The algebric apparatus associated with this result allows us to prove the following two results. The first one is the characterization of real multiplicative functions f(n), with 0<=f(p)<1, as minimal values of certain quadratic forms on the t(N) units sphere. The second one is the explicit evaluation of the minimal values of certain others quadratic forms also on the units sphere
- …
