2015•arXiv (Cornell University)Open access
Explicit refinements of B\\"ocherer's conjecture for Siegel modular forms\n of squarefree level
Martin Dickson, Ameya Pitale, Abhishek Saha, Ralf Schmidt
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Abstract
We formulate an explicit refinement of B\\"ocherer's conjecture for Siegel\nmodular forms of degree 2 and squarefree level, relating weighted averages of\nFourier coefficients with special values of L-functions. To achieve this, we\ncompute the relevant local integrals that appear in the refined global\nGan-Gross-Prasad conjecture for Bessel periods as proposed by Yifeng Liu. We\nnote several consequences of our conjecture to arithmetic and analytic\nproperties of L-functions and Fourier coefficients of Siegel modular forms.\n
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