186,493 research outputs found
Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms
Full text linkIn 1961, Rankin determined the asymptotic behavior of the number
of positive integers for which a given prime does not divide the -th divisor sum function.
By computing the associated Euler-Kronecker constant which depends on the arithmetic of certain subfields of ,
we obtain the second order term in the asymptotic expansion of
Using a method developed by Ford, Luca and Moree (2014),
we determine the pairs with
for which Ramanujan's
approximation to is better than Landau's.
This entails checking
whether or not, and requires a substantial computational number theoretic input and extensive computer usage.
We apply our results to study the non-divisibility of Fourier coefficients of six
cusp forms by certain exceptional primes, extending the earlier work of Moree (2004), who disproved several
claims made by Ramanujan on the non-divisibility of
the Ramanujan tau function by five such exceptional primes
AGY-6778 | Moree Fire Station
No full text<p>Moree Fire Station was established by 1914 and registered as fire station No. 381. (1) <br /><br />It was part of Zone Regional North 3 - Peel and, in 2015, the address was 179 Balo Street, Moree. (2)<br /><br />Endnotes <br />1. NRS 19883<br />2. NSW Fire and Rescue <a href="http://www.fire.nsw.gov.au/station_details.php?id=202">http://www.fire.nsw.gov.au/station_details.php?id=202</a> (accessed 27 October 2015)</p>
Influence of Conservation of Native Vegetation on Land Values in Moree Plains Shire, NSW
Full text linkThe Native Vegetation Conservation Act was introduced on January 1st 1998 to protect native grassland and woodland in New South Wales. The Act has limited clearing of native vegetation and development to crops and pasture, has protected biodiversity, and may have enhanced soil and water conservation. But an analysis of variations in the prices paid for farm land in Moree Plains Shire, with the complementary hedonic and bargaining methods, shows how buyers, sellers, and the market as a whole, value the characteristics of the land. It shows that the Act has led to substantial losses in land values for the farmers. The Act has imposed higher costs on those who had kept most vegetation, and on those who most need to retain their options to clear and develop. Stewardship payments will alleviate the financial situation for some and property plans will provide long-term security for both farmer and vegetation. But the magnitudes of the losses suggest that introduction of individual policies like these must be preceded by a review of the whole strategy of vegetation protection in New South Wales. We must first decide how much to protect and how to allocate the losses in an equitable manner.Environmental Economics and Policy, Land Economics/Use,
Euler constants from primes in arithmetic progression
Full text linkMany Dirichlet series of number theoretic interest can be written as a
product of generating series , with ranging over all the primes in the
primitive residue class modulo , and a function well-behaved
around . In such a case the corresponding Euler constant can be expressed
in terms of the Euler constants of the series
involved and the (numerically more harmless) term . Here we
systematically study , their numerical evaluation and discuss some
examples
Computation of the Kummer ratio of the class number for prime cyclotomic fields
No full textWe introduce an algorithm to compute , the ratio between ,
Kummer's emph{first factor of the class number} of ,
and its expected order of magnitude ,
where is an odd prime number and is a primitive -root of unity.
Such an algorithm requires products together with logarithm evaluations.
We obtain a new maximum for , namely ,
see section
ef{chi-Bernoulli-method} below.
The program used and the results here described are collected
at the following address \url{http://www.math.unipd.it/~languasc/rq-comput.html}
A combinatorial identity arising from cobordism theory
Full text linkLet . Let be the vector obtained from by deleting the entries and . A. Besser and P. Moree [Arch. Math. (Basel) 79 (2002), no. 6, 463--471; MR1967264 (2004a:11014)] introduced some invariants and near invariants related to the solutions \underline\epsilon\in\{\pm1}^{m-2} of the linear inequality , where denotes the usual inner product and the vector obtained from by deleting and . The main result of [op. cit.] is extended here to a much more general setting, namely that of certain maps from finite sets to
On the distribution of the order and index of g (mod p) over residue classes. I
No full textAbstractFor a fixed rational number g∉{−1,0,1} and integers a and d we consider the sets Ng(a,d), respectively Rg(a,d), of primes p for which the order, respectively the index of g(modp) is congruent to a(modd). Under the Generalized Riemann Hypothesis (GRH), it is known that these sets have a natural density δg(a,d), respectively ρg(a,d). It is shown that these densities can be expressed as linear combinations of certain constants introduced by Pappalardi. Furthermore it is proved that δg(a,d) and ρg(a,d) equal their g-averages for almost all g
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
Convoluted convolved Fibonacci numbers
No full textAbstract The convolved Fibonacci numbers F (r) In this note we consider some related numbers that can be expressed in terms of convolved Fibonacci numbers. These numbers appear in the numerical evaluation of a constant arising in the study of the average density of elements in a finite field having order congruent to a (mod d). We derive a formula expressing these numbers in terms of ordinary Fibonacci and Lucas numbers. The non-negativity of these numbers can be inferred from Witt's dimension formula for free Lie algebras. This note is a case study of the transform (with f any formal series), which was introduced and studied in a companion paper by Moree
- …
