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math.NT2025
On twisted period functions and Moments of a weighted mean square of Dirichlet L-functions on the critical line
Sebastien Darses, Berend Ringeling, Emmanuel Royer
We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties -- including Eisenstein series and period functions -- that were…
math.NT2014
The amplification method in the GL(3) Hecke algebra
Roman Holowinsky, Guillaume Ricotta, Emmanuel Royer
This article contains all of the technical ingredients required to implement an effective, explicit and unconditional amplifier in the context of GL(3) automorphic forms. In partic…
math.NT2014
Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two (with an Appendix by E. Kowalski and A. Saha)
Emmanuel Royer, Jyoti Sengupta, Jie Wu
In this paper, we show that half of non-zero coefficients of the spinor zeta function of a Siegel cusp form of genus 2 are positive and half are negative.