论文标题
在Gross-Prasad的猜想上，其改进为$ \ left（\ mathrm {so} \ left（5 \ right），\ mathrm {so} \ left（2 \ right）\ right）$和广义的böcherer猜想
On the Gross-Prasad conjecture with its refinement for $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$ and the generalized Böcherer conjecture
论文作者
论文摘要
在$ \ left的情况下，我们研究了毛sad的猜想及其对贝塞尔期间的改进（\ mathrm {so} \ left（5 \ right），\ mathrm {so} \ left（2 \ weled（2 \ right）\ right）$。特别是，通过结合几个theta对应关系，我们证明了用于任何可恢复不可约的尖齿式体型表示的Ichino-ikeda型公式。作为我们公式的推论，我们证明了一个明确的公式，该公式将一定的加权平均值与全态Siegel siegel cusp形式的傅立叶系数二级形式与$ l $ functions的中心特价值与中心特价值相关。该公式被认为是Böcherer猜想对非平凡的环形特征案例的自然概括。
We investigate the Gross-Prasad conjecture and its refinement for the Bessel periods in the case of $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$. In particular, by combining several theta correspondences, we prove the Ichino-Ikeda type formula for any tempered irreducible cuspidal automorphic representations. As a corollary of our formula, we prove an explicit formula relating certain weighted averages of Fourier coefficients of holomorphic Siegel cusp forms of degree two which are Hecke eigenforms to central special values of $L$-functions. The formula is regarded as a natural generalization of the Böcherer conjecture to the non-trivial toroidal character case.
