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

Emmanuel Royer (1) , Jyoti Sengupta (2) , Jie Wu (3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 MU - University of Mumbai
3 IECL - Institut Élie Cartan de Lorraine

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

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.327 - 339. ⟨10.1142/S1793042113500966⟩. ⟨hal-01093998⟩