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pro vyhledávání: '"33C20"'
The combination of recent results due to Yu and Chen [Proc. AMS 150(4), 2020, 1749-1765] and to Bostan and Yurkevich [Proc. AMS 150(5), 2022, 2131-2136] shows that the 3-D Euclidean shape of the square Clifford torus is uniquely determined by its iso
Externí odkaz:
http://arxiv.org/abs/2411.05643
Autor:
Hang, Peng-Cheng
Recently, Hang and Luo (2024) used an elementary approach to derive the leading asymptotic behavior of the Humbert function $\Psi_1[a,b;c,c';x,y]$ when $x\to\infty$ and $y\to +\infty$. In this paper, we give detailed asymptotic analyses of $\Psi_1$ w
Externí odkaz:
http://arxiv.org/abs/2410.21985
Autor:
Wang, Haoming
In this paper, we introduce the matrix normal distribution according to the tensor decomposition of its covariance. Based on the canonical diagonal form, the moment generating function of sample covariance matrix and the distribution of latent roots
Externí odkaz:
http://arxiv.org/abs/2410.14490
Autor:
Kocar, Mutlu, Tanabe, Susumu
We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are expressed by Melli
Externí odkaz:
http://arxiv.org/abs/2409.16459
Autor:
Zahaf, Mohammed Brahim, Mesk, Mohammed
The aim of this work is to characterize all generating functions of the form $A(t)F(xtA(t)-R(t))$ for the classical orthogonal polynomials. Further generating functions are also provided by derivation.
Externí odkaz:
http://arxiv.org/abs/2409.16034
Autor:
Ikeda, Karin, Kadono, Yuta
The central binomial series is a subject that has been extensively studied, for example in the context of the irrationality of Riemann zeta values. In this paper, the Hurwitz version of the central binomial series is defined by adding one real parame
Externí odkaz:
http://arxiv.org/abs/2409.16026
This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks in 1934 in the Annals of Mathematics. The
Externí odkaz:
http://arxiv.org/abs/2409.14512
Autor:
Zudilin, Wadim
Given a newform with the Fourier expansion $\sum_{n=1}^\infty b(n)q^n\in\mathbb Z[[q]]$, a prime $p$ is said to be non-ordinary if $p\mid b(p)$. We exemplify several newforms of weight 4 for which the latter divisibility implies a stronger divisibili
Externí odkaz:
http://arxiv.org/abs/2409.00384
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the bicomplex holom
Externí odkaz:
http://arxiv.org/abs/2408.13246
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite fields, a theo
Externí odkaz:
http://arxiv.org/abs/2408.02918