Results 31 to 40 of about 891 (145)
Canonical Labeling of Latin Squares in Average‐Case Polynomial Time
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT A Latin square of order n$$ n $$ is an n×n$$ n\times n $$ matrix in which each row and column contains each of n$$ n $$ symbols exactly once. For ε>0$$ \varepsilon >0 $$, we show that with high probability a uniformly random Latin square of order n$$ n $$ has no proper subsquare of order larger than n1/2log1/2+εn$$ {n}^{1/2}{\log}^{1/2 ...
Michael J. Gill +2 more
wiley +1 more source
Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms
, 2010 A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a ...
A. Enneper +40 more
core +1 more source
Prime values of Ramanujan's tau function
, 2023 We study the prime values of Ramanujan's tau function $τ(n)$. Lehmer found that $n=251^2=63001$ is the smallest $n$ such that $τ(n)$ is prime: $$τ(251^2)=-80561663527802406257321747.$$ We prove that in most arithmetic progressions (mod 23), the prime values $τ$ belonging to the progression form a thin set. As a consequence, there exists a set of primes
openaire +2 more sources
Arithmetic constants for symplectic variances of the divisor function
Mathematika, Volume 71, Issue 3, July 2025.Abstract Kuperberg and Lalín stated some conjectures on the variance of certain sums of the divisor function dk(n)$d_k(n)$ over number fields, which were inspired by analogous results over function fields proven by the authors. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to
Vivian Kuperberg, Matilde Lalín
wiley +1 more source
Lp$L^p$‐norm bounds for automorphic forms via spectral reciprocity
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract Let g$g$ be a Hecke–Maaß cusp form on the modular surface SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$, namely an L2$L^2$‐normalised non‐constant Laplacian eigenfunction on SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$ that is additionally a joint eigenfunction of every Hecke operator. We prove the L4$L^
Peter Humphries, Rizwanur Khan
wiley +1 more source
Restart Perturbations for Reversible Markov Chains: Trichotomy and Pre‐Cutoff Equivalence
Random Structures &Algorithms, Volume 66, Issue 3, May 2025.ABSTRACT Given a reversible Markov chain Pn$$ {P}_n $$ on n$$ n $$ states, and another chain P˜n$$ {\tilde{P}}_n $$ obtained by perturbing each row of Pn$$ {P}_n $$ by at most αn$$ {\alpha}_n $$ in total variation, we study the total variation distance between the two stationary distributions, ‖πn−π˜n‖$$ \left\Vert {\pi}_n-{\tilde{\pi}}_n\right\Vert $$.
Daniel Vial, Vijay Subramanian
wiley +1 more source
On the Typical Size and Cancelations Among the Coefficients of Some Modular Forms [PDF]
, 2013 We obtain a nontrivial upper bound for almost all elements of the sequences of real numbers which are multiplicative and at the prime indices are distributed according to the Sato--Tate density.
Luca, Florian +2 more
core +1 more source
On the density of the odd values of the partition function, II: An infinite conjectural framework
, 2018 We continue our study of a basic but seemingly intractable problem in integer partition theory, namely the conjecture that $p(n)$ is odd exactly $50\%$ of the time.
Judge, Samuel D., Zanello, Fabrizio
core +1 more source
Journal of Geophysical Research: Planets, Volume 130, Issue 5, May 2025.Abstract Extracting additional information from old or incomplete fireball data sets remains a challenge. To address missing point‐by‐point observations, we introduce a method for estimating atmospheric flight parameters of meteoroids using metaheuristic optimization techniques.
Eloy Peña‐Asensio, Maria Gritsevich
wiley +1 more source
The Carlson‐type zero‐density theorem for the Beurling ζ$\zeta$ function
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract In a previous paper, we proved a Carlson‐type density theorem for zeroes in the critical strip for the Beurling zeta functions satisfying Axiom A of Knopfmacher. There we needed to invoke two additional conditions: the integrality of the norm (Condition B) and an “average Ramanujan condition” for the arithmetical function counting the number ...
Szilárd Gy. Révész
wiley +1 more source