Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
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Reliability as Projection in Operator-Theoretic Test Theory: Conditional Expectation, Hilbert Space Geometry, and Implications for Psychometric Practice. [PDF]
Educ Psychol MeasZumbo BD.
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Non‐vanishing of Poincaré series on average
Mathematika, Volume 72, Issue 2, April 2026.Abstract We study when Poincaré series for congruence subgroups do not vanish identically. We show that almost all Poincaré series with suitable parameters do not vanish when either the weight k$k$ or the index m$m$ varies in a dyadic interval. Crucially, analyzing the problem ‘on average’ over these weights or indices allows us to prove non‐vanishing ...
Ned Carmichael, Noam Kimmel
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MF-IEKF: A Multiplicative Federated Invariant Extended Kalman Filter for INS/GNSS. [PDF]
Sensors (Basel)Zhao L, Chen T, Yuan P, Li X, Luo Y.
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Discrepancy of arithmetic progressions in boxes and convex bodies
Mathematika, Volume 72, Issue 2, April 2026.Abstract The combinatorial discrepancy of arithmetic progressions inside [N]:={1,…,N}$[N]:= \lbrace 1, \ldots, N\rbrace$ is the smallest integer D$D$ for which [N]$[N]$ can be colored with two colors so that any arithmetic progression in [N]$[N]$ contains at most D$D$ more elements from one color class than the other.
Lily Li, Aleksandar Nikolov
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Direct Products for the Hamiltonian Density Property. [PDF]
J Geom AnalAndrist RB, Huang G.
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
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Complex Time Approach to the Hamiltonian and the Entropy Production of the Damped Harmonic Oscillator. [PDF]
Entropy (Basel)Aslani KE.
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Variants of a theorem of Macbeath in finite‐dimensional normed spaces
Mathematika, Volume 72, Issue 2, April 2026.Abstract A classical theorem of Macbeath states that for any integers d⩾2$d \geqslant 2$, n⩾d+1$n \geqslant d+1$, d$d$‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with n$n$ vertices.
Zsolt Lángi, Shanshan Wang
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Plug-and-play computational method for advancing natural and biomedical image representation. [PDF]
Patterns (N Y)Gong H, Han T, Li G.
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