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。通过分解Eichler-Shimura类型的积分，他还发现了一种从一大类的自同构型得到上同调类的直接方法。他将自己的研究成果整理成一本书，由美国数学学会出版。他与博士生Kashio Tomokazu Kashio合作，研究了绝对CM周期的p-进类似物。有强有力的证据表明，p-进类似物以一种完美的方式成立。几年前，池田构造了一个从椭圆模形式到多元Siegel模形式的升维。他以提升对角线的限制为核函数，构造了一个新的提升，其中宫城提升为特例。他提出了一个猜想，将这种提升的不零性与某些L函数的特殊值联系起来。Hiraga提出了一个猜想，该猜想与Arthur猜想的Zlevinskii对合和A包有关。作为证据，他证明了内窥镜提升和Zlevinskii对合的可交换性。他进一步研究了亚瑟关于自同构表示的猜想。Umeda研究了关于经典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、与其他生成系统的关系和生成系统的显式表示。这些问题源于Capelli恒等式，也就是不变微分算子的恒等式。藤原利用泰勒-怀尔斯-藤原理论研究了利奥波尔特猜想，并得出了这个数字的新观点。场和双曲流形是相似的。Fujii研究了关于Riemann Zeta函数的自变量的零、蒙哥马利和和的高阶矩的配对相关性的蒙哥马利猜想。

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.