Definite orthogonal modular forms: computations, excursions, and discoveries [0.03%]
确定性的正交模形式：计算、漫游和发现
Eran Assaf,Dan Fretwell,Colin Ingalls et al.
Eran Assaf et al.
We consider spaces of modular forms attached to definite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators defined by Kneser neighbours. After reviewing algorithms to compute with these spaces, we invest...
On the Mordell-Weil lattice of [Formula: see text] in characteristic 3 [0.03%]
特征为3时Mordell-Weil晶格上的[formula: see text]
Gauthier Leterrier
Gauthier Leterrier
We study the elliptic curves given by y 2 = x 3 + b x + t 3 n + 1 over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain supe...
A Density of Ramified Primes [0.03%]
分歧素数的密度
Stephanie Chan,Christine McMeekin,Djordjo Milovic
Stephanie Chan
Let K be a cyclic number field of odd degree over Q with odd narrow class number, such that 2 is inert in K / Q . We define a family of number fields { K ( p ) } p , depending on K and indexed by the rational primes p that split complete...
Irreducibility of limits of Galois representations of Saito-Kurokawa type [0.03%]
塞托- kurakawa类型的伽罗瓦表示的极限的不可约性
Tobias Berger,Krzysztof Klosin
Tobias Berger
We prove (under certain assumptions) the irreducibility of the limit σ 2 of a sequence of irreducible essentially self-dual Galois representations σ k : G Q → GL 4 ( Q ¯ p ) (as k approaches 2 in a p-adic sense) w...
Gabriel A Dill
Gabriel A Dill
We count algebraic numbers of fixed degree d and fixed (absolute multiplicative Weil) height H with precisely k conjugates that lie inside the open unit disk. We also count the number of values up to H that the height assumes on algebraic n...
Robert Tichy,Ingrid Vukusic,Daodao Yang et al.
Robert Tichy et al.
Let { U n } n ≥ 0 and { V m } m ≥ 0 be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [ - x , x ] which can be represented as differences U n - V m . In pa...
Paul Surer
Paul Surer
We present the zeta-expansion as a complex version of the well-known beta-expansion. It allows us to expand complex numbers with respect to a complex base by using integer digits. Our concepts fits into the framework of the recently publish...
An explicit form of the polynomial part of a restricted partition function [0.03%]
限制性分区函数的多项式部分的显式形式
Karl Dilcher,Christophe Vignat
Karl Dilcher
We prove an explicit formula for the polynomial part of a restricted partition function, also known as the first Sylvester wave. This is achieved by way of some identities for higher-order Bernoulli polynomials, one of which is analogous to...
Vandita Patel,Samir Siksek
Vandita Patel
Let k ≥ 2 be even, and let r be a non-zero integer. We show that for almost all d ≥ 2 (in the sense of natural density), the equation x k + ( x + r ) k + ⋯ + ( x + ( d - 1 ) r ) k = y n , x , y , n ∈ Z , n ...
Decomposition types in minimally tamely ramified extensions of [Formula: see text] [0.03%]
最小温和奇点扩张中的分解类型公式大小正确公式大小正确公式大小正确
David S Dummit,Hershy Kisilevsky
David S Dummit
We examine whether it is possible to realize finite groups G as Galois groups of minimally tamely ramified extensions of Q and also specify both the inertia groups and the further decomposition of the ramified primes. ...