王者体育

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bessel functions and beyond endoscopy

qizhi bairenjihuayanjiuyuan (zhejiangdaxue)

in this talk, i will first introduce the thesis of akshay venkatesh on beyond endoscopy for $\mathrm{sym}^2$ $l$-functions on $\mathrm{gl}_2$ over $\mathbb{q}$ or a totally real field. the idea follows a suggestion of peter sarnak on using the kuznetsov relative trace formula instead of the arthur-selberg trace formula for the beyond endoscopy problem. i will then discuss how to generalize venkatesh's work from totally real to arbitrary number fields. the main supplement is an integral formula for the fourier transform of bessel functions over $\mathbb{c}$.