Research on special values and zeros of L-funcions and on automorphic forms

吉田研究了围绕绝对CM周期的各种问题。此外，他发现了一个直接的方法来获得上同调类自守形式的一个广泛的类，通过分解积分的艾希勒志村型。他把自己的研究成果整理成册，由美国数学学会出版。他与博士生Tomokazu Kashio合作研究了绝对CM周期的p-adic模拟。有强有力的证据表明，一个p-adic模拟举行了一个完美的方式。几年前，Ikeda构造了一个从多元椭圆模形式到Siegel模形式的生命。作为核函数的限制对角线的这种提升，他构造了一个新的生活，其中包含宫胁的提升作为一个特殊的情况。他制定了一个猜想，涉及非零的这一解除特殊价值的某些L-职能。Hiraga提出了一个猜想，它将Zelevinskii对合与亚瑟提出的A-包联系起来。作为证据，他证明了内窥镜升降机和Zelevinskii对合的可交换性。他进一步研究了亚瑟猜想的自守表示。Umeda研究了经典型李代数的泛包络代数中心的三个问题，即生成系统的具体描述、与其它生成系统的关系以及生成系统的显式表示。这些问题起源于不变微分算子的恒等式Capelli恒等式。藤原用泰勒-怀尔斯-藤原理论研究了利奥波德猜想，得出了数的新观点。场和双曲流形是类似的。藤井研究了蒙哥马利猜想对相关的零，蒙哥马利和高'时刻的论点黎曼zeta函数。

Yoshida studied various problems centered around the absolute CM-period. Also he found a direct method to obtain cohomology classes from automorphic forms of a wide class, by decomposing the integral of Eichler-Shimura type. He organized his research results in a book, which was published by American Mathematical Society. He studied a p-adic analogue of the absolute CM-period, in collaboration with Ph. D student Tomokazu Kashio. There are strong evidences that a p-adic analogue holds in a perfect manner. A few years ago, Ikeda constructed a lifing from elliptic modular forms to Siegel modular forms of several variables. Taking as the kernel function the restriction to the diagonal of this lifting, he constructed a new lifing, which contains Miyawaki's lifting as a apecial case.. He formulated a conjecture which relates the nonvanishing of this lifting to special values of certain L-functions. Hiraga formulated a conjecture which relates the Zelevinskii involution and A-packet conjectured by Arthur. As an evidence, he proved the commutativity of endoscopic lifts and the Zelevinskii involution. He further studied Arthur's conjecture 'on automorphic representations. Umeda studied three problems on the center of the univeral enveloping algebra of a Lie algebra of classical type, namely concrete description of generating system, relations to the other generating system and explicit representations of a generation system. These problems originated from the Capelli identity which is the identity of invariant differential operators. Fujiwara studied Leopoldt's conjecture using the Taylor-Wiles-Fujiwara theory and arrived at the new point of view that number. fields and hyperbolic manifolds are analogous. Fujii studied on the Montgomery conjecture on the pair correlations of zeros, the Montgomery sum and higher 'moments of the argument of the Riemann zeta function.