On the refined Gan-Gross-Prasad conjecture for cusp forms of GSp(4)

Jun Wen

On the refined Gan-Gross-Prasad conjecture for cusp forms of GSp(4)

Number Theory 2016-06-14 v4

Authors: Jun Wen

Abstract

We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$ -value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups $(\SO(5), \SO(2))$ . The conjecture has been previously proved for certain automorphic forms on $\mathrm{GSp_4}$ from lifts. In this paper, we extend the formula to Siegel modular forms of $\Sp_4(\bZ)$ .

Keywords

Gan-Gross-Prasad conjecture cusp forms GSp(4) Bessel period central L-value Siegel modular forms automorphic forms

Cite

@article{arxiv.1512.09222,
  title  = {On the refined Gan-Gross-Prasad conjecture for cusp forms of GSp(4)},
  author = {Jun Wen},
  journal= {arXiv preprint arXiv:1512.09222},
  year   = {2016}
}

Comments

fix constant 1/8; discuss the global L-function. arXiv admin note: text overlap with arXiv:1510.07334

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