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pro vyhledávání: '"Lukas Spiegelhofer"'
Autor:
LUKAS SPIEGELHOFER
Publikováno v:
Journal of the Australian Mathematical Society. 114:110-144
The Thue–Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors w within this sequence, or more precisely, the sequence of gaps between consecutive occurre
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https://explore.openaire.eu/search/publication?articleId=doi_________::5ec6f7d9fe9f1421bb58cae8ec2e9aae
https://doi.org/10.1017/s1446788721000380
https://doi.org/10.1017/s1446788721000380
Publikováno v:
International Journal of Number Theory. 18:955-976
Résumé. Pour deux entiers [Formula: see text], nous posons [Formula: see text] et [Formula: see text] (où [Formula: see text]) et nous notons respectivement [Formula: see text] et [Formula: see text] les fonctions sommes des chiffres dans les [For
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https://doi.org/10.1142/s1793042122500506
https://doi.org/10.1142/s1793042122500506
Autor:
Lukas Spiegelhofer
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 172:139-161
Let S be the sum-of-digits function in base 2, which returns the number of 1s in the base-2 expansion of a nonnegative integer. For a nonnegative integer t, define the asymptotic density $${c_t} = \mathop {\lim }\limits_{N \to \infty } {1 \over N}|\{
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https://doi.org/10.1017/s0305004121000153
https://doi.org/10.1017/s0305004121000153
Autor:
Lukas Spiegelhofer
Publikováno v:
Compositio Mathematica. 156:2560-2587
The level of distribution of a complex valued sequence $b$ measures "how well $b$ behaves" on arithmetic progressions $nd+a$. Determining whether $\theta$ is a level of distribution for $b$ involves summing a certain error over $d\leq D$, where $D$ d
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14035547e3e1c43f59a25e01650bd952
https://doi.org/10.1112/s0010437x20007563
https://doi.org/10.1112/s0010437x20007563
Autor:
Lukas Spiegelhofer, Michael Wallner
Publikováno v:
Journal of Number Theory. 192:221-239
For nonnegative integers $j$ and $n$ let $\Theta(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are not divisible by $2^{j+1}$. In this paper we prove that the family $j\mapsto\Theta(j,n)$ usually follows a normal distribu
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7202227dec7655778b40d542c956cd5c
https://doi.org/10.1016/j.jnt.2018.04.010
https://doi.org/10.1016/j.jnt.2018.04.010
Publikováno v:
Proceedings of the American Mathematical Society. 146:3679-3691
We show that the (morphic) sequence ( − 1 ) s φ ( n ) (-1)^{s_\varphi (n)} is asymptotically orthogonal to all bounded multiplicative functions, where s φ s_\varphi denotes the Zeckendorf sum-of-digits function. In particular we have ∑ n > N (
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https://explore.openaire.eu/search/publication?articleId=doi_________::777f8d28f9d5c16dc6a0421e608a1be0
https://doi.org/10.1090/proc/14015
https://doi.org/10.1090/proc/14015
Autor:
Lukas Spiegelhofer, Michael Wallner
The binary sum-of-digits function $s$ counts the number of ones in the binary expansion of a nonnegative integer. For any nonnegative integer $t$, T.~W.~Cusick defined the asymptotic density $c_t$ of integers $n\geq 0$ such that \[s(n+t)\geq s(n).\]
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4152aeb78acea9a5610da0f0b997d9bb
Autor:
Lukas Spiegelhofer, Thomas Stoll
Publikováno v:
Mosc. J. Comb. Number Theory 9, no. 1 (2020), 43-49
Moscow Journal of Combinatorics and Number Theory
Moscow Journal of Combinatorics and Number Theory, 2020, Vol. 9 (No. 1), pp.43-49. ⟨10.2140/moscow.2020.9.43⟩
Moscow Journal of Combinatorics and Number Theory
Moscow Journal of Combinatorics and Number Theory, 2020, Vol. 9 (No. 1), pp.43-49. ⟨10.2140/moscow.2020.9.43⟩
Let $s_2$ be the sum-of-digits function in base $2$, which returns the number of non-zero binary digits of a nonnegative integer $n$. We study $s_2$ alon g arithmetic subsequences and show that --- up to a shift --- the set of $m$-tuples of integers
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http://arxiv.org/abs/1909.08849
http://arxiv.org/abs/1909.08849
Autor:
Michael Wallner, Lukas Spiegelhofer
Publikováno v:
The Electronic Journal of Combinatorics. 26
The Tu–Deng Conjecture is concerned with the sum of digits $w(n)$ of $n$ in base $2$ (the Hamming weight of the binary expansion of $n$) and states the following: assume that $k$ is a positive integer and$1\leqslant t
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https://doi.org/10.37236/7178
https://doi.org/10.37236/7178
Autor:
Michael Wallner, Lukas Spiegelhofer
Publikováno v:
Acta Arithmetica. 181:27-55
For a prime $p$ and nonnegative integers $j$ and $n$ let $\vartheta_p(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are exactly divisible by $p^j$. Moreover, for a finite sequence $w=(w_{r-1}\cdots w_0)\neq (0,\ldots,0)$
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https://doi.org/10.4064/aa8524-6-2017
https://doi.org/10.4064/aa8524-6-2017