Published in Forum Mathematicum
Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determ...
Published in Forum Mathematicum
Recently, the problem of bounding the sup norms of L2{L^{2}}-normalized cuspidal automorphic newforms ϕ on GL2{\mathrm{GL}_{2}} in the level aspect has received much attention. However at the moment strong upper bounds are only available if the central character χ of ϕ is not too highly ramified. In this paper, we establish a uniform upper bound in...
Published in Forum Mathematicum
We prove Deligne’s conjecture for symmetric fifth L-functions of elliptic newforms of weight greater than 5. As a consequence, we establish period relations between motivic periods associated to an elliptic newform and the Betti–Whittaker periods of its symmetric cube functorial lift to GL4{\operatorname{GL}_{4}}.
Published in Forum Mathematicum
By old results with Millson, the generating series for the cohomology classes of special cycles on orthogonal Shimura varieties over a totally real field are Hilbert–Siegel modular forms. These forms arise via theta series. Using this result and the Siegel–Weil formula, we show that the products in the subring of cohomology generated by the special...
Published in Forum Mathematicum
The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality 𝔪{\mathfrak{m}} whose proper subgroups of cardinality 𝔪{\mathfrak{m}} are (bounded) Engel groups. It is proved that such groups are (bounded) Engel groups, provided that they satisfy some generalized solubility condition. A similar analysis is carrie...
Published in Forum Mathematicum
We investigate the relative opers over the complex analytic family of compact complex manifolds of relative dimension one. We introduce the notion of relative opers arising from the second fundamental form associated with a relative holomorphic connection. We also investigate the relative differential operators over the complex analytic family of c...
Published in Forum Mathematicum
In this paper we continue our investigations of 4-dimensional complexes in [A. Cavicchioli, F. Hegenbarth, F. Spaggiari, Four-dimensional complexes with fundamental class, Mediterr. J. Math. 17 (2020), 175]. We study a class of finite oriented 4-complexes which we call FC4{\mathrm{FC}_{4}}-complexes, defined as follows. An FC4{\mathrm{FC}_{4}}-comp...
Published in Forum Mathematicum
In [J. P. Keating, B. Rodgers, E. Roditty-Gershon and Z. Rudnick, Sums of divisor functions in 𝔽q[t]\mathbb{F}_{q}[t] and matrix integrals, Math. Z. 288 2018, 1–2, 167–198], the authors established relationships of the mean-square of sums of the divisor function dk(f){d_{k}(f)} over short intervals and over arithmetic progressions for the functio...
Published in Forum Mathematicum
Let ψ:ℕ→ℝ+{\psi:\mathbb{N}\to\mathbb{R}^{+}} be a function satisfying ϕ(n)n→∞{\frac{\phi(n)}{n}\to\infty} as n→∞{n\to\infty}. We investigate from a multifractal analysis point of view the growth rate of the sums ∑k=1nlogak(x){\sum^{n}_{k=1}\log a_{k}(x)} relative to ψ(n){\psi(n)}, where [a1(x),a2(x),…]{[a_{1}(x),a_{2}(x),\dots]} denotes the c...
Published in Forum Mathematicum
For a variable Z=(zij){Z=(z_{ij})} of the Siegel upper half space Hn{H_{n}} of degree n, put ∂Z=(1+δij2∂∂zij)1≤i,j≤n{{\partial}_{Z}=(\frac{1+\delta_{ij}}{2}\frac{{\partial}}{{\partial}z_{ij}})_{% 1\leq i,j\leq n}}. For a polynomial P(T){P(T)} in components of n×n{n\times n} symmetric matrix T, we have P(∂Z)det(Z)s=det(Z)sQ(Z-1){P({\part...
