Results 11 to 20 of about 6,964 (137)
When are two Dedekind sums equal?
, 2011 A natural question about Dedekind sums is to find conditions on the integers $a_1, a_2$, and $b$ such that $s(a_1,b) = s(a_2, b)$. We prove that if the former equality holds then $ b \ | \ (a_1a_2-1)(a_1-a_2)$.
Jabuka, Stanislav +2 more
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In Defense of Comparability: Reply to Carlson and Risberg
Noûs, EarlyView.ABSTRACT In “The Case for Comparability,” we argue that every comparative expression “F$F$” obeys Comparability: if two things are at least as F$F$ as themselves, then one of them must be at least as F$F$ as the other. One of our arguments appeals to the apparent validity of the Strong Monotonicity schema: x$x$ is F$F$; y$y$ is not F$F$; so, x$x$ is ...
Cian Dorr, Jacob M. Nebel, Jake Zuehl
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Philosophy and Phenomenological Research, EarlyView.ABSTRACT Determinism is (roughly) the thesis that the past determines the future. But efforts to define it precisely have exposed deep methodological disagreements. Standard possible‐worlds formulations of determinism presuppose an “agreement” relation between worlds, but this relation can be understood in multiple ways, none of which is particularly ...
Hans Halvorson +2 more
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The largest values of Dedekind sums
, 2016 Let $s(m,n)$ denote the classical \DED sum, where $n$ is a positive integer and $m\in\{0,1,\ldots, n-1\}$, $(m,n)=1$. For a given positive integer $k$, we describe a set of at most $k^2$ numbers $m$ for which $s(m,n)$ may be $\ge s(k,n)$, provided that ...
Girstmair, Kurt
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Journal of Number Theory, 1996 For a positive integer k and an arbitrary integer h, the Dedekind sum s(h,k) was first studied by Dedekind because of the prominent role it plays in the transformation theory of the Dedekind eta-function, which is a modular form of weight 1/2 for the full modular group SL_2(Z). There is an extensive literature about the Dedekind sums.
Conrey, J. B. +3 more
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
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Spherical Casimir energies and Dedekind sums
, 2004 Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's.
Beck M +14 more
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Dedekind Sums and Lambert Series [PDF]
Proceedings of the American Mathematical Society, 1954 In this note the author gives an elementary proof of the transformation formula for \(f(k,h,\tau)\) (see the review Zbl 0057.03701) by making use of the representation of \(c_r(h,k)\) by means of Euler numbers.
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Generalized Dedekind sums [PDF]
Geometry and Topology Monographs, 2004 Classical Dedekind sums are connected to the modular group through the construction of a (Dedekind) symbol on the cusp set of the modular group. In this paper we study generalizations of Dedekind symbols and sums that can be associated to certain Fuchsian groups uniformizing 1-punctured tori.
Long, D. D., Reid, A. W.
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A classification of Prüfer domains of integer‐valued polynomials on algebras
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
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