发表机构
IIT Bhubaneswar; University of Oklahoma; Queen Mary University of London; University of North Texas（印度理工学院布巴内斯瓦尔分校; 俄克拉荷马大学; 伦敦玛丽女王大学; 北德克萨斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对Sp₄的傅里叶-雅可比周期，在新分歧情形下计算相关局部积分，构建了关联二次西格尔尖型形式与半整数权形式Petersson范数的显式猜想恒等式，并指出其在范数增长等方面的推论。
AI 中文摘要
我们在新的分歧情形下计算了Sp₄的傅里叶-雅可比周期的改进Gan--Gross--Prasad猜想中出现的局部积分，并用此来构建一个显式的猜想性恒等式，该恒等式将二次西格尔尖型形式的Petersson范数与相关的半整数权形式联系起来。我们指出该恒等式对Petersson范数增长、傅里叶系数大小以及中心L值非零性的推论。
英文摘要
We compute the local integrals appearing in the refined Gan--Gross--Prasad conjecture for Fourier--Jacobi periods of $\mathrm{Sp}_4$ in new ramified cases and use this to formulate an explicit conjectural identity relating Petersson norms of degree 2 Siegel cusp forms and associated half-integral weight forms. We note consequences of our identity for the growth of Petersson norms, the size of Fourier coefficients, and non-vanishing of central $L$-values.
CommentsIssues related to absolute convergence have been fixed; constant in main theorem has been corrected; Link to Lean formalization of part of the local calculations has been added
