日時：２０１８年７月１９日（木）１３：３０から
場所：金沢大学サテライトプラザ ２階講義室
（北陸数論セミナーと併催)
７月１９日（木）
13:30 -- 14:30 平野 雄一（東京大学）
TBA
14:50 -- 15:50 Soma Purkait（東京理科大学）
Local Hecke algebras and newforms
16:10 -- 17:10 鈴木 美裕（京都大学）
Quaternion distinguished representations and base change for unitary groups
17:30 -- 18:30 Kimball Martin（オクラホマ大学）
The basis problem
19:00 -- 懇親会
平野 雄一（東京大学）
タイトル: TBA
Abstract: TBA
Soma Purkait（東京理科大学）
タイトル: Local Hecke algebras and newforms
アブストラクト:
We describe genuine Hecke algebras of the double cover of SL_2(Q_p) with respect to certain open compact subgroups by generators and relations. We use these to define classical Hecke operators on the space of cuspidal modular forms of weight k+1/2 and level M where M is odd and square-free. We consider a subspace that is common -1 eigenspace of certain finitely many pair of conjugate operators and show that this subspace is Hecke isomorphic to the space of newforms of weight 2k and level 4M.
鈴木 美裕（京都大学）
タイトル: Quaternion distinguished representations and base change for unitary groups
アブストラクト:
Base change lift is a conjectural map from the set of cuspidal automorphic representations of a unitary group to the set of automorphic representations of a general linear group. Flicker and Rallis conjectured that a cuspidal automorphic representation of GL is in the image of the base change lift if and only if it is distinguished with respect to certain subgroup. Considering quaternion distinguished representations, we will propose a slight generalization of this conjecture and prove it for GL(2) by using a relative trace formula.
Kimball Martin（オクラホマ大学）
タイトル: The basis problem
アブストラクト:
The basis problem, studied in depth by Eichler and others, asks what spaces of modular forms can be generated by theta series, especially theta series attached to quaternion algebras. We will discuss a representation-theoretic approach to this problem using the Jacquet-Langlands correspondence. This approach both refines the solution to the basis problem by Hijikata-Pizer-Shemanske for elliptic modular forms and solves the basis problem for Hilbert modular forms. This has applications to computing spaces of modular forms and exhibiting congruences.
この研究集会はJSPS外国人招へい研究者（短期）（被招へい研究者 Kimball Martin）の調査研究費によって援助を受けています。
世話人: 若槻 聡（金沢大学）