Results 51 to 60 of about 12,032 (167)
Nagoya Mathematical Journal, 1996 For positive integers h, k and m, the higher-order Dedekind sums are defined ...
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Where Mathematical Symbols Come From
Topics in Cognitive Science, Volume 18, Issue 1, Page 169-186, January 2026.Abstract There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ‘+$+$’ or ‘8’ by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice.
Dirk Schlimm
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Torsion classes of extended Dynkin quivers over commutative rings
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract For a Noetherian R$R$‐algebra Λ$\Lambda$, there is a canonical inclusion torsΛ→∏p∈SpecRtors(κ(p)Λ)$\mathop {\mathsf {tors}}\Lambda \rightarrow \prod _{\mathfrak {p}\in \operatorname{Spec}R}\mathop {\mathsf {tors}}(\kappa (\mathfrak {p})\Lambda)$, and each element in the image satisfies a certain compatibility condition.
Osamu Iyama, Yuta Kimura
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On the Product of Zeta-Functions
MathematicsIn this paper, we study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference α, an integer with the Voronoĭ function weight Vk.
Nianliang Wang +2 more
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Dedekind sums with even denominators
Journal of Number Theory, 2019 Let $S(a,b)$ denote the normalized Dedekind sum. We study the range of possible values for $S(a,b)=\frac{k}{q}$ with $\gcd(k,q)=1$. Girstmair proved local restrictions on $k$ depending on $q\pmod{12}$ and whether $q$ is a square and conjectured that these are the only restrictions possible.
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Generalized Dedekind eta-functions and generalized Dedekind sums [PDF]
Transactions of the American Mathematical Society, 1973 A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.
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Nontriviality of rings of integral‐valued polynomials
Mathematische Nachrichten, Volume 298, Issue 12, Page 3974-3994, December 2025.Abstract Let S$S$ be a subset of Z¯$\overline{\mathbb {Z}}$, the ring of all algebraic integers. A polynomial f∈Q[X]$f \in \mathbb {Q}[X]$ is said to be integral‐valued on S$S$ if f(s)∈Z¯$f(s) \in \overline{\mathbb {Z}}$ for all s∈S$s \in S$. The set IntQ(S,Z¯)${\mathrm{Int}}_{\mathbb{Q}}(S,\bar{\mathbb{Z}})$ of all integral‐valued polynomials on S$S ...
Giulio Peruginelli, Nicholas J. Werner
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Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization
MathematicsWe consider a wide class of summatory functions Ff;N,pm=∑k≤Nfpmk, m∈Z+∪{0} associated with the multiplicative arithmetic functions f of a scaled variable k∈Z+, where p is a prime number. Assuming an asymptotic behavior of the summatory function, F{f;N,1}=
Leonid G. Fel
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Dedekind sums: A combinatorial-geometric viewpoint [PDF]
, 2004 11 ...
Matthias Beck, Sinai Robins
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The Silent Shift: Investigating Selenium Biovolatilization in Natural Environments
Reviews of Geophysics, Volume 63, Issue 4, December 2025.Abstract Selenium (Se) is essential for human health. Organisms produce volatile Se through metabolism, which is an essential but hidden component of the Se geochemical cycle. Understanding this natural cycle is vital for sustainable development and ecosystem protection, thereby preserving planetary health and fostering harmonious coexistence between ...
Ruixuan Zhang +5 more
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