函数Sp(n2)与Sp(n)的关系

对于任意正整数n,设幂p的原数函数Sp(n)定义为Sp(n)=min{m:pn|m!},其中p为素数.本文目的是运用初等方法研究函数Sp(n2)与Sp(n)之间的关系,并得到一个有趣的恒等式.     

Odd character degrees for Sp(2n,2)

We check the McKay conjecture on character degrees for the case of symplectic groups over the field with two elements ${\mathrm{Sp}}_{2n}(2)$ and the prime 2. Then we check the inductive McKay condition (Isaacs–Malle–Navarro) for ${\mathrm{Sp}}_4(2^m)$ and all primes.     

Invariants of the group Sp6(2)

We find the Poincaré series of the rings of invariants of the symmetric algebras of 7and 15-dimensional representations of the group Sp₆(2).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 94, pp. 70–72, 1979.     

Extensions of Simple Modules for Sp4(2n) and Suz(2m)

The group of extensions between any two irreducible 2-modularrepresentations of the groups Sp₄ (2ⁿ) and Suz (2^m) is determined.     

Superfield Quantization in the Sp(2)-Covariant Formalism

We generalize the rules for the superfield Sp(2)-covariant quantization of arbitrary gauge theories to the case of gauge fixing by the generating equations for the gauge functional. We consider possible realizations of the extended antibrackets and show that only one of the realizations is consistent with the extended BRST symmetry transformations in the form of the supertranslations along the Grassmann coordinates of a superspace.     

关于Dirichlet L-函数的2k次加权均值

本文的主要目的是利用特征和估计及其三角和方法研究Dirichlet L-函数的2k次加权均值，并得到了一个较为精确的渐近公式。     

Similarity over Sp(2n,Z)

This section appears in nearly every issue. Send admission to R.C. Thompson, at the the Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.     

Similarity over Sp(2n,Z)

This section appears in nearly every issue. Send admission to R.C. Thompson, at the the Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.     

一个关于原数函数Sp(n)的恒等式

对于任意给定的素数p及正整数n,我们定义幂p的原数函数Sp(n)为最小的正整数m使得pn|m!.即就是:Sp(n)=min{m:pn|m!}.本文的主要目的是利用初等方法研究函数Sp(n)的算术性质,并得到一个有趣的恒等式.     

The classification and curvature of biquotients of the form Sp(3)/\!\!/Sp(1)^2

We show there are precisely \(15\) inhomogeneous biquotients of the form \(Sp(3)/\!\!/Sp(1)^2\) and show that at least \(8\) of them admit metrics of quasi-positive curvature.     

The Classification of Exponential Paths in Sp(2)

众所周知，四阶以上辛群中指数型道路的Ｍａｓｌｏｖ指标可以取任意整数．本文给出了二阶辛群中指数型道路的分类及其Ｍａｓｌｏｖ指标的取值范围，指出了与高阶情形的不同之处．     

齐性空间SU(2n)/Sp(n)的H-同伦指数

令p为大于3的素数.在一定维数限制下,通过把齐性空间SU(2n)/Sp(n)分解为若干个同伦可结合,同伦可交换的H-空间的乘积,进而得到了SU(2n)/Sp(n)的p素H-同伦指数的一个上界.     

On the modularity of the GL<Subscript>2</Subscript>-twisted spinor L-function

In modern number theory there are famous theorems on the modularity of Dirichlet series attached to geometric or arithmetic objects. There is Hecke’s converse theorem, Wiles proof of the Taniyama-Shimura conjecture, and Fermat’s Last Theorem to name a few. In this article in the spirit of the Langlands philosophy we raise the question on the modularity of the GL₂-twisted spinor L-function Z _{G ⊗ h} (s) related to automorphic forms G,h on the symplectic group GSp₂ and GL₂. This leads to several promising results and finally culminates into a precise very general conjecture. This gives new insights into the Miyawaki conjecture on spinor L-functions of modular forms. We indicate how this topic is related to Ramakrishnan’s work on the modularity of the Rankin-Selberg L-series.