共查询到20条相似文献，搜索用时 23 毫秒
1.
Wolfgang Müller 《Monatshefte für Mathematik》1999,44(2):315-330
Denote by the number of points of the lattice in the “blown up” domain , where is a convex body in () whose boundary is smooth and has nonzero curvature throughout. It is proved that for every fixed
where for and . This improves a classic result of E. Hlawka [8] and its refinements due to E. Kr?tzel and W. G. Nowak ([14], [15]). The proof uses a multidimensional variant of the method of van der Corput for the estimation of exponential
sums. 相似文献
2.
Dominique Barbolosi 《Monatshefte für Mathematik》1999,128(3):189-200
For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. GALAMBOS proved that (μ the Gauss measure)
In this paper, we first point out that for all , ( has no limit for for almost all , proving more precisely that: For all , one has for almost all
Then we prove mainly the more precise result: For all , the sequence has no subsequence which converges almost everywhere.
(Re?u le 4 mai 1998; en forme révisée le 25 février 1999) 相似文献
3.
Clemens Heuberger 《Monatshefte für Mathematik》2001,132(4):325-339
In a recent paper [7] the author considered the family of parametrized Thue equations
for monic polynomials which satisfy
Under some technical conditions it could be proved that there is a computable constant such that for all integers the only integer solutions of the Diophantine equation satisfy .
In this paper, we give an explicit expression for depending on the polynomials .
(Received 5 September 2000; in revised form 30 December 2000) 相似文献
4.
We establish a new bound for the exponential sum
where λ is an element of the residue ring modulo a large prime number
and
are arbitrary subsets of the residue ring modulo p − 1 and γ (n) are any complex numbers with | γ (n)| ≦ 1.
Received: 15 June 2005 相似文献
5.
B. R. Schratzberger 《Monatshefte für Mathematik》2001,134(2):143-157
We show that for the three-dimensional multiplicative Brun’s algorithm, the exponent of convergence is , i.e. there is a such that for almost all ,
(Received 15 January 2001; in revised form 4 May 2001) 相似文献
6.
Dominique Barbolosi 《Monatshefte für Mathematik》1999,28(4):189-200
For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. GALAMBOS proved that (μ the Gauss measure)
In this paper, we first point out that for all , ( has no limit for for almost all , proving more precisely that: For all , one has for almost all
相似文献
7.
In this paper we completely solve the family of Thue equations
where is an integral parameter. In particular, for , the only solutions are the trivial ones with x = 0 or y = 0. The result is achieved by sharpening the estimates of part I of the paper and by solving Thue equations with the method of Bilu and Hanrot.
(Received 25 January 2000; in revised form 10 April 2000) 相似文献
8.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
We also show that
where ω(n) is the number of distinct prime divisors of n and p denotes prime numbers. These estimates improve several results from [6, 9].
Received: 23 November 2006 相似文献
9.
Xiaojing Yang 《Archiv der Mathematik》2005,85(5):460-469
In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator
is discussed, where α, β are positive constants satisfying
for some ω ∈R+ /Q, h(t) ∈L∞ [0, 2π ] is 2π-periodic, x±=max {±x, 0 }.
Received: 23 September 2004 相似文献
10.
Aleksandar Ivić 《Archiv der Mathematik》2008,90(5):412-419
If
denotes the error term in the classical Rankin-Selberg problem, then it is proved that
where Δ1(x) = ∫
x
0 Δ(u)du. The latter bound is, up to ‘ɛ’, best possible.
Received: 8 February 2007 相似文献
11.
Jie Wu 《Monatshefte für Mathematik》2002,135(1):69-81
We prove that under the Riemann hypothesis one has for any ,
This improves a result of Zhai and Cao, which requires 11/30 in place of 221/608.
Received 28 May 2001 相似文献
12.
R. Nair 《Monatshefte für Mathematik》2001,132(4):341-348
Let ? be a class of real valued integrable functions on [0,1). We will call a strictly increasing sequence of natural numbers
an sequence if for every f in ? we have
almost everywhere with respect to Lebesgue measure. Here, for a real number y we have used to denote the fractional part of y. For a finite set A we use to denote its cardinality. In this paper we show that for strictly increasing sequences of natural numbers and , both of which are sequences for all , if there exists such that
then the sequence of products of pairs of elements in a and b once ordered by size is also an sequence.
(Received 2 March 2000; in revised form 3 January 2001) 相似文献
13.
J. Schoißengeier 《Monatshefte für Mathematik》2000,131(3):227-234
For a real number x let be the fractional part of x and for any set M let c
M
be the characteristic function of M. For and a positive integer N let
be the discrepancy of the sequence modulo 1. In this paper we prove that
(Received 2 May 2000; in revised form 19 June 2000) 相似文献
14.
elements of some (finite) poset , write for the probability that precedes in a random (uniform) linear extension of . For define
where the infimum is over all choices of and distinct .
Addressing an issue raised by Fishburn [6], we give the first nontrivial lower bounds on the function . This is part of a more general geometric result, the exact determination of the function
where the infimum is over chosen uniformly from some compact convex subset of a Euclidean space.
These results are mainly based on the Brunn–Minkowski Theorem and a theorem of Keith Ball [1], which allow us to reduce to
a 2-dimensional version of the problem.
Received: October 6, 1997 相似文献
15.
16.
In this report we detail the following story. Several centuries ago, Abel noticed that the well-known elementary integral
is just an augur of more surprising integrals of the shape
Here f is a polynomial of degree g and the D are certain polynomials of degree deg . Specifically, (so q divides ). Note that, morally, one expects such integrals to produce inverse elliptic functions and worse, rather than an innocent
logarithm of an algebraic function.
Abel went on to study, well, abelian integrals, and it is Chebychev who explains – using continued fractions – what is going
on with these ‘quasi-elliptic’ integrals. Recently, the second author computed all the polynomials D over the rationals of degree 4 that have an f as above. We will explain various contexts in which the present issues arise. Those contexts include symbolic integration
of algebraic functions; the study of units in function fields; and, given a suitable polynomial g, the consideration of period length of the continued fraction expansion of the numbers as n varies in the integers. But the major content of this survey is an introduction to period continued fractions in hyperelliptic
– thus quadratic – function fields.
(Received 7 December 1999; in revised form 29 April 2000) 相似文献
17.
E.G. Coffman Jr. George S. Lueker Joel Spencer Peter M. Winkler 《Probability Theory and Related Fields》2001,120(4):585-599
A random rectangle is the product of two independent random intervals, each being the interval between two random points
drawn independently and uniformly from [0,1]. We prove that te number C
n
of items in a maximum cardinality disjoint subset of n random rectangles satisfies
where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that, for some absolute constat K,
Finally, for a certain distribution of random cubes we show that for some absolute constant K, the number Q
n
of items in a maximum cardinality disjoint subset of the cubes satisies
Received: 1 September 1999 / Revised version: 3 November 2000 / Published online: 14 June 2001 相似文献
18.
Filip Saidak 《Archiv der Mathematik》2005,85(4):345-361
Assuming a quasi Generalized Riemann Hypothesis (quasi-GRH for short) for Dedekind zeta functions over Kummer fields of the
type
we prove the following prime analogue of a conjecture of Erd?s & Pomerance (1985) concerning the exponent function fa(p) (defined to be the minimal exponent e for which ae ≡ 1 modulo p):
where
The main result is obtained by computing all the higher moments corresponding to ω(fa(p)), and by comparing them, via the Fréchet-Shohat theorem, with estimates due to Halberstam concerning the moments of ω(p − 1).
Received: 25 October 2004; revised: 12 February 2005 相似文献
| ((‡)) |
19.
Let K be a field of characteristic 0 and let p, q, G
0
, G
1
, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G
n
(x))
n=0
∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G
n
(x) = G
m
(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we
present also bounds for the cardinality of the set
In the last part we specialize our results to certain families of orthogonal polynomials.
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT.
The second author was supported by the Hungarian National Foundation for Scientific Research Grants No 16741 and 38225.
Received June 5, 2001; in revised form February 26, 2002
RID="a"
ID="a" Dedicated to Edmund Hlawka on the occasion of his 85th birthday 相似文献
20.
Wen-Bin Zhang 《Mathematische Annalen》2007,337(3):671-704
Two Beurling generalized number systems, both with and k > 0, are constructed. The associated zeta function of the first satisfies the RH and its prime counting function satisfies
π(x) = li (x) + O(x
1/2). The associated zeta function of the second has infinitely many zeros on the curve σ = 1−1/log t and no zeros to the right of the curve and the Chebyshev function ψ(x) of its primes satisfies
and
A sharpened form of the Diamond–Montgomery–Vorhauer random approximation and elements of analytic number theory are used
in the construction. 相似文献