Asymptotic number of points on certain ellipsoids

1972 ◽  
Vol 11 (6) ◽  
pp. 381-386
Author(s):  
E. P. Golubeva
Keyword(s):  
Asymptotic Number

scholarly journals On the Zeros of a Class of Canonical Products of Integral Order

1963 ◽  
Vol 13 (3) ◽  
pp. 247-253 ◽  
Author(s):  
N. A. Bowen
Keyword(s):  
Asymptotic Formula ◽  
Asymptotic Behaviour ◽  
Canonical Product ◽  
Number Of Zeros ◽  
Asymptotic Number ◽  
Canonical Products ◽  
Analogous Theorem ◽  
Single Radius ◽  
Integral Order

In (1) I obtained † an asymptotic formula for the number of zeros of an arbitrary canonical product II(z) of integral order but not of mean type, all of whose zeros lie on a single radius, from a knowledge of the asymptotic behaviour of (i)log | П(z)| as | z | = r→ ∞ along another radius l, with certain side conditions. After proving the analogous theorem in which log | П(z)| in (i) is replaced by , I show in this note that, at a cost of replacing l by two radii l1 and l2, both of these theorems may be generalised to include a class of canonical products of integral order whose zeros lie along a whole line. In one of the resulting theorems ‡ (Theorem II) I find the asymptotic number of zeros on each half of the line of zeros; another theorem (Theorem III) includes a previous result of mine.§

The Asymptotic Number of Unlabelled Regular Graphs

1982 ◽  
Vol s2-26 (2) ◽  
pp. 201-206 ◽  
Author(s):  
Béla Bollobás
Keyword(s):  
Regular Graphs ◽  
Asymptotic Number

scholarly journals The asymptotic number of labeled graphs with given degree sequences

1978 ◽  
Vol 24 (3) ◽  
pp. 296-307 ◽  
Author(s):  
Edward A Bender ◽  
E.Rodney Canfield
Keyword(s):  
Degree Sequences ◽  
Labeled Graphs ◽  
Asymptotic Number

scholarly journals The asymptotic number of integral cubic polynomials with bounded heights and discriminants

2014 ◽  
Vol 54 (2) ◽  
pp. 150-165 ◽  
Author(s):  
Dzianis Kaliada ◽  
Friedrich Götze ◽  
Olga Kukso
Keyword(s):  
Asymptotic Number ◽  
Cubic Polynomials

scholarly journals PRIMES REPRESENTED BY INCOMPLETE NORM FORMS

2020 ◽  
Vol 8 ◽  
Author(s):  
JAMES MAYNARD
Keyword(s):  
Algebraic Geometry ◽  
Irreducible Polynomial ◽  
Type I ◽  
Type Ii ◽  
Geometry Of Numbers ◽  
Asymptotic Number ◽  
Special Case

Let $K=\mathbb{Q}(\unicode[STIX]{x1D714})$ with $\unicode[STIX]{x1D714}$ the root of a degree $n$ monic irreducible polynomial $f\in \mathbb{Z}[X]$ . We show that the degree $n$ polynomial $N(\sum _{i=1}^{n-k}x_{i}\unicode[STIX]{x1D714}^{i-1})$ in $n-k$ variables takes the expected asymptotic number of prime values if $n\geqslant 4k$ . In the special case $K=\mathbb{Q}(\sqrt[n]{\unicode[STIX]{x1D703}})$ , we show that $N(\sum _{i=1}^{n-k}x_{i}\sqrt[n]{\unicode[STIX]{x1D703}^{i-1}})$ takes infinitely many prime values, provided $n\geqslant 22k/7$ . Our proof relies on using suitable ‘Type I’ and ‘Type II’ estimates in Harman’s sieve, which are established in a similar overall manner to the previous work of Friedlander and Iwaniec on prime values of $X^{2}+Y^{4}$ and of Heath-Brown on $X^{3}+2Y^{3}$ . Our proof ultimately relies on employing explicit elementary estimates from the geometry of numbers and algebraic geometry to control the number of highly skewed lattices appearing in our final estimates.

scholarly journals ANALYTIC METHODS FOR SELECT SETS

2012 ◽  
Vol 26 (4) ◽  
pp. 561-568 ◽  
Author(s):  
J. Gaither ◽  
M.D. Ward
Keyword(s):  
Selection Procedure ◽  
Expected Number ◽  
Asymptotic Growth ◽  
First Order ◽  
Analytic Methods ◽  
Asymptotic Number

We analyze the asymptotic number of items chosen in a selection procedure. The procedure selects items whose rank among all previous applicants is within the best 100p percent of the number of previously selected items. We use analytic methods to obtain a succinct formula for the first-order asymptotic growth of the expected number of items chosen by the procedure.

scholarly journals ‘The Asymptotic Number of Connected d-Uniform Hypergraphs’ — CORRIGENDUM

2014 ◽  
Vol 24 (1) ◽  
pp. 373-375 ◽  
Author(s):  
MICHAEL BEHRISCH ◽  
AMIN COJA-OGHLAN ◽  
MIHYUN KANG
Keyword(s):  
Uniform Hypergraphs ◽  
Asymptotic Number ◽  
Made In

The authors would like to rectify a mistake made in Theorem 1.1 of their article (Behrisch, Cojaa-Oghlan & Kang 2014), published in issue 23 (3). The text below explains the changes required.

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