A symplectic restriction problem

2019/12/16 by Blomer, Valentin, Corbett, Andrew · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.07496

Abstract

We investigate the norm of a degree 2 Siegel modular form of asymptotically large weight whose argument is restricted to the 3-dimensional subspace of its imaginary part. On average over Saito-Kurokawa lifts an asymptotic formula is established that is consistent with the mass equidistribution conjecture on the Siegel upper half space as well as the Lindelof hypothesis for the corresponding Koecher-Maass series. The ingredients include a new relative trace formula for pairs of Heegner periods.

Cited by

• Cusp forms of weight 1/2 and pairs of quadratic forms
• The hyperbolic circle problem over Heegner points

Related

• A Restriction Norm Problem for Siegel Modular Forms
• Weighted equidistribution theorem for Siegel modular forms of degree 2
• Mass equidistribution for Saito-Kurokawa lifts
• Large values of modular forms
• The weight reduction of mod p Siegel modular forms for GSp₄