arXiv subjects

Hidenori Katsurada

Publications and source records attributed to Hidenori Katsurada.

21 records · Page 2Linked to original sources

arXiv2011

On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups

We prove a formula of Petersson's type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficient. The method in this paper is essentially a generalization of Kitaoka's previous work which studied the full modular case, but some modification is necessary to obtain estimates which are sharp with respect to the level aspect.

math.NT↗

arXiv2011

Congruence between Duke-Imamoglu-Ikeda lifts and non-Duke-Imamoglu-Ikeda lifts

Let k and n be positive even integers. For a cuspidal Hecke eigenform g in the Kohnen plus subspace of weight k-n/2+1/2 and level 4, let I(g) be the Duke-Imamoglu-Ikeda lift of g in the space of cusp forms of weight k for Sp(n,Z), and f the primitive form of weight 2k-n for SL(2,Z) corresponding to g under the Shimura correspondence. We then characterize prime ideals giving congruence between I(g) and another cuspidal Hecke eigenform not coming from the Duke-Imamoglu-Ikeda lift in terms of the specilal values of the Hecke L-function and the adjoint L-function of f.

math.NT↗

arXiv2005

Genus theta series, Hecke operators and the basis problem for Eisenstein series

We derive explicit formulas for the action of the Hecke operator $T(p)$ on the genus theta series of a positive definite integral quadratic form and prove a theorem on the generation of spaces of Eisenstein series by genus theta series. We also discuss connections of our results with Kudla's matching principle for theta integrals.

math.NT↗