Sign changes in short intervals of coefficients of spinor zeta function of a Siegel cusp form of genus 2

Emmanuel Royer (1) , Jyoti Sengupta , Jie Wu

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this paper, we establish a Voronoi formula for the spinor zeta function of a Siegel cusp form of genus 2. We deduce from this formula quantitative results on the number of its positive (resp. negative) coefficients in some short intervals.

Mots clés: Spinor zeta function; Voronoi formula; Fourier coefficients; Siegel form

Domaines: Théorie des nombres [math.NT]

Emmanuel Royer, Jyoti Sengupta, Jie Wu. Sign changes in short intervals of coefficients of spinor zeta function of a Siegel cusp form of genus 2. International Journal of Number Theory, 2014, 10 (2), pp.297-306. ⟨10.1142/S1793042113500966⟩. ⟨hal-00800984v2⟩