Results 51 to 60 of about 25,597,246 (186)
Bounded exponential sums with multiplicative coefficients
Mathematika, Volume 72, Issue 4, October 2026.Abstract We investigate when the exponential sum Sf(x,α):=∑n⩽xf(n)e(nα)$S_f(x,\alpha) := \sum _{n\leqslant x}f(n)\mathrm{e}(n\alpha)$ is bounded, for a multiplicative function f$f$ and α∈R$\alpha \in \mathbb {R}$. We show that under natural assumptions, Sf(x,α)$S_f(x,\alpha)$ is bounded only when f$f$ is very close to a twisted Dirichlet character χ(n ...
Péa Bazin, Ihor Pylaiev, Fred Tyrrell
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On $p$-adic valuations of Stirling numbers
Acta Arithmetica, 2018 The Stirling number of the second kind (or Stirling partition number) which are denoted by \(S(n,k)\) have many applications in mathematics, and particularly in combinatorics. \(S(n,k)\) is the number of ways to partition a set of $n$ objects into \(k\) non-empty ones.
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On the Existential Theory of the Completions of a Global Field
Mathematische Nachrichten, Volume 299, Issue 9, Page 2680-2692, September 2026.ABSTRACT We discuss the common existential theory of all or almost all completions of a global function field.
Philip Dittmann, Arno Fehm
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p-adic orthogonal wavelet bases
, 2009 We describe all MRA-based p-adic compactly supported wavelet systems forming an orthogonal basis for L 2(ℚ p ).
Shelkovich, V. M. +2 more
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Comptes Rendus. MathématiqueWe prove some triviality results for reduced Whitehead groups and reduced unitary Whitehead groups for division algebras over a Henselian discrete valuation field whose residue field has virtual cohomological dimension or separable dimension $\le 2 ...
Hu, Yong, Tian, Yisheng
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A note on p-adic valuations of Schenker sums [PDF]
Colloquium Mathematicum, 2015 A prime number p is called a Schenker prime if there exists such n ∈ N+ that p n and p | an, where an = ∑n j=0 n! j! n j is a socalled Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning p-adic valuations of an in case when p is a Schenker prime.
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Modular analogs of character formulas and minimal lifts of modular forms
Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.Abstract If f$f$ is a mod‐3 eigenform of weight 2 and level Γ0(ℓ2)$\Gamma _0(\ell ^2)$ for a prime ℓ$\ell$ such that ℓ≡−1(mod3)$\ell \equiv -1 \pmod {3}$, and ℓ$\ell$ is a vexing prime for f$f$, we show that there is no obstruction to finding a minimal lift of f$f$, but that there is an obstruction to finding a nonminimal lift.
Patrick B. Allen, Preston Wake
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On alternative definition of Lucas atoms and their p-adic valuations
Monatshefte für MathematikAbstract Lucas atoms are irreducible factors of Lucas polynomials and they were introduced in Sagan and Tirrell (Adv Math 374:107387, 2020). The main aim of the authors was to investigate, from an innovatory point of view, when some combinatorial rational functions are actually polynomials.
Alecci, Gessica +3 more
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h$h$‐Function, Hilbert–Kunz density function and Frobenius–Poincaré function
Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.Abstract Given ideals I,J$I,J$ of a noetherian local ring (R,m)$(R, \mathfrak {m})$ such that I+J$I+J$ is m$\mathfrak {m}$‐primary and a finitely generated R$R$‐module M$M$, we associate an invariant of (M,R,I,J)$(M,R,I,J)$ called the h$h$‐function.
Cheng Meng, Alapan Mukhopadhyay
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A possible p-adic Weber-Fechner law
, 2018 From a simple extension of a previous formal pattern of unconscious-conscious interconnection based on the representation of mental entities by m-adic numbers through hysteresis phenomenology, a pattern which has been then used to work out a possible ...
Iurato, Giuseppe,
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