Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Balazard, Michel"'
Autor:
Balazard, Michel, Martin, Bruno
The average value of the smallest denominator of a rational number belonging to the interval $](j-1)/N,j/N]$, where~$j=1,\dots, N$, is proved to be asymptotically equivalent to~$16\pi^{-2}\sqrt{N}$, when $N$ tends to infinity. The result had been con
Externí odkaz:
http://arxiv.org/abs/2303.01303
Autor:
Balazard, Michel
Publikováno v:
Number Theory. Dedicated to the memory of Eduard Wirsing, Springer, In press
A study of the greatest possible ratio of the smallest absolute value of a higher derivative of some function, defined on a bounded interval, to the L p-norm of the function.
Externí odkaz:
http://arxiv.org/abs/2211.07196
Autor:
Balazard, Michel
This expository article is an introduction to Landau's problem of bounding the derivative, knowing bounds for the function and its second derivative, and some of its variants and generalizations. Connexions with convex and functional analysis, numeri
Externí odkaz:
http://arxiv.org/abs/2005.09318
Autor:
Balazard, Michel, Martin, Bruno
Publikováno v:
Mathematische Zeitschrift, Springer, A para{\^i}tre
The Brjuno function attains a strict global minimum at the golden section.
Comment: in French
Comment: in French
Externí odkaz:
http://arxiv.org/abs/2002.04471
Let $b > a > 0$. We prove the following asymptotic formula $$\sum_{n\ge 0} \big\lvert\{x/(n+a)\} - \{x/(n+b)\}\big\rvert = \frac{2}{\pi}\zeta(3/2)\sqrt{cx} + O(c^{2/9}x^{4/9}),$$ with $c=b-a$, uniformly for $x \ge 40 c^{-5}(1+b)^{27/2}$.
Comment
Comment
Externí odkaz:
http://arxiv.org/abs/1907.09768
Autor:
Balazard, Michel
In this mainly expository article, we revisit some formal aspects of B{\'a}ez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function $\nu$, which is e
Externí odkaz:
http://arxiv.org/abs/1812.04309
Autor:
Balazard, Michel
A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian Toeplitz-multiplicative dete
Externí odkaz:
http://arxiv.org/abs/1809.08868
Autor:
Balazard, Michel, Martin, Bruno
In the line of classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. This allows us to reprove, among others, a convergence criterion for a
Externí odkaz:
http://arxiv.org/abs/1807.05719
Autor:
Balazard, Michel
We give an asymptotic formula for the quadratic total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers.
Comment: in French
Comment: in French
Externí odkaz:
http://arxiv.org/abs/1606.03377
Autor:
Balazard, Michel
We give an asymptotic formula for the total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers.
Comment: in French, A para\^itre au (to appear in) Moscow Journal of Combina
Comment: in French, A para\^itre au (to appear in) Moscow Journal of Combina
Externí odkaz:
http://arxiv.org/abs/1606.03378