Mohamed Alaa Tawfik,Rachel Newton
Mohamed Alaa Tawfik
Let E and E ' be elliptic curves over Q with complex multiplication by the ring of integers of an imaginary quadratic field K and let Y = Kum ( E × E ' ) be the minimal desingularisation of the quotient of E × E ' by the act...
Asymptotics of commuting [Formula: see text] -tuples in symmetric groups and log-concavity [0.03%]
对称群中渐近 commute 的[公式]元组的渐近性质及其与对数凹性的关系
Kathrin Bringmann,Johann Franke,Bernhard Heim
Kathrin Bringmann
Denote by N ℓ ( n ) the number of ℓ -tuples of elements in the symmetric group S n with commuting components, normalized by the order of S n . In this paper, we prove asymptotic formulas for N ℓ ( n ) . In addition...
Sebastian Heintze,Volker Ziegler
Sebastian Heintze
In this paper, we consider the Diophantine equation Vn-bm=c for given integers b, c with b≥2, whereas Vn varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation ...
Walter Bridges,Kathrin Bringmann
Walter Bridges
In this paper, we prove that the number of unimodal sequences of size n is log-concave. These are coefficients of a mixed false modular form and have a Rademacher-type exact formula due to recent work of the second author and Nazaroglu on f...
Giacomo Micheli,Severin Schraven,Simran Tinani et al.
Giacomo Micheli et al.
The geometric sieve for densities is a very convenient tool proposed by Poonen and Stoll (and independently by Ekedahl) to compute the density of a given subset of the integers. In this paper we provide an effective criterion to find all hi...
Vlad Serban
Vlad Serban
We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F . In particular, given a finitely generated subgroup Γ of F...
Cameron Franc,Geoffrey Mason
Cameron Franc
We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a p-adic Banach space replaces the traditional Hilbert space. We study some consequences of ...
Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang [0.03%]
过分割函数对数的高阶差分的不等式及Wang-Xie-Zhang问题
Gargi Mukherjee
Gargi Mukherjee
Let p ¯ ( n ) denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., ( - 1 ) r - 1 Δ r log p ...
Harald Andrés Helfgott,Lola Thompson
Harald Andrés Helfgott
We present a new elementary algorithm that takes time O ϵ x 3 5 ( log x ) 8 5 + ϵ and space O x 3 10 ( log x ) 13 10 (measured bitwise) for computing M ( x ) = ∑ n ≤ x μ ( n ) , where μ ( n...
Sudhir Pujahari,Neelam Saikia
Sudhir Pujahari
Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and...