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Modules of Jacobi forms of degree two of small levels
Hiroki Aoki, Tomoyoshi Ibukiyama
The purpose of this paper is to describe explicitly the modules of (Siegel-)Jacobi forms of degree two of index one of any scalar valued weight with respect to some congruence subg…
Hermitian modular forms and algebraic modular forms on
Tomoyoshi Ibukiyama, Brandon Williams
We state conjectures that relate Hermitian modular forms of degree two and algebraic modular forms for the compact group . We provide evidence for these conjectures in the f…
Formal series of Jacobi forms
Hiroki Aoki, Tomoyoshi Ibukiyama, Cris Poor
We prove for general paramodular level that formal series of scalar Jacobi forms with an involution condition necessarily converge and are therefore the Fourier-Jacobi expansions a…
Period of the Ikeda-Miyawaki lift
Tomoyoshi Ibukiyama, Hidenori Katsurada, Hisashi Kojima
In this paper, first we give a weak version of Ikeda's conjecture on the period of the Ikeda-Miyawaki lift. Next, we confirm this conjecture rigorously in some cases.
Harder's conjecture II
Hiraku Atobe, Masataka Chida, Tomoyoshi Ibukiyama +2
Let be a primitive form of weight for , and let be a prime ideal of the Hecke field of . We denote by the Siegel modular group of degree .…
Genus character -functions of quadratic orders in an adelic way and maximal orders of matrix algebras
Tomoyoshi Ibukiyama
For a quadratic extension of , we consider orders in that are not necessarily maximal and the ideal class group in the narrow sense of proper ide…
Dimensions of paramodular forms and compact twist modular forms with involutions
Tomoyoshi Ibukiyama
We give an explicit dimension formula for paramodular forms of degree two of prime level with plus or minus sign of the Atkin--Lehner involution of weight $\det^k\operatorname{Sym}…
When is a polarised abelian variety determined by its -divisible group?
Tomoyoshi Ibukiyama, Valentijn Karemaker, Chia-Fu Yu
We study the Siegel modular variety of genus and its supersingular locus . As our main result we determine precis…
Harder's conjecture I
Hiraku Atobe, Masataka Chida, Tomoyoshi Ibukiyama +2
Let be a primitive form with respect to . Then we propose a conjecture on the congruence between the Klingen-Eisenstein lift of the Duke-Imamoglu-Ikeda lift of and…
Eisenstein congruences for SO(4,3), SO(4,4), spinor and triple product L-values
Jonas Bergström, Neil Dummigan, Thomas Mégarbané
We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of…
Jacobi forms that characterize paramodular forms
Tomoyoshi Ibukiyama, Cris Poor, David S. Yuen
The Fourier Jacobi expansions of paramodular forms are characterized from among all formal series of Jacobi forms by two conditions on the Fourier coeffcients of the Jacobi forms:…