Elvira Lupoian,James Rawson
Elvira Lupoian
In this paper we give an algorithm to find the 3-torsion subgroup of the Jacobian of a smooth plane quartic curve with a marked rational point. We describe 3 - torsion points in terms of cubics which triply intersect the curve, and use thi...
A Fourier-Jacobi Dirichlet series for cusp forms on orthogonal groups [0.03%]
正交群上尖形式的傅里叶-雅可比Dirichlet级数
Rafail Psyroukis
Rafail Psyroukis
We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms F, G for orthogonal groups of signature ( 2 , n + 2 ) . In the case when F is a Hecke eigenform and G is a Maass lift of a Poincaré series, we e...
Harry Spencer
Harry Spencer
Mazur and Rubin introduced the notion of n-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by t ∈ Z ...
Traces of partition Eisenstein series and almost holomorphic modular forms [0.03%]
分区Eisenstein级数的迹和几乎全域模形式
Kathrin Bringmann,Badri Vishal Pandey
Kathrin Bringmann
Recently, Amdeberhan, Griffin, Ono, and Singh started the study of "traces of partition Eisenstein series" and used it to give explicit formulas for many interesting functions. In this note we determine the precise spaces in which they lie,...
On p-refined Friedberg-Jacquet integrals and the classical symplectic locus in the [Formula: see text] eigenvariety [0.03%]
关于p- refined的Friedberg-Jacquet积分以及[Formula: see text]胚丛中经典的辛簇
Daniel Barrera Salazar,Andrew Graham,Chris Williams
Daniel Barrera Salazar
Friedberg-Jacquet proved that if π is a cuspidal automorphic representation of GL 2 n ( A ) , then π is a functorial transfer from GSpin 2 n + 1 if and only if a global zeta integral Z H over H = GL n × GL n is non-v...
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...