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تسجيل مستخدم جديدتحويل نماذج هيلبرت-سايغل الجنس 2 في $Q(sqrt{5})$ عبر التطابق جاكيه-لانجلاندس
Computing genus 2 Hilbert-Siegel modular forms over $Q(sqrt{5})$ via the Jacquet-Langlands correspondence
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في هذه الورقة، نقدم خوارزمية لحساب نظم الأيجنستيم الخاصة بالشكل الحجري الحلبيرت-سايجل لحقول المربعة الريالية الذاتية الثنائية من عدد الفئة الضيقة واحد. نعطي بعض الأمثلة البيانية باستخدام الحقل الثنائي $Q(sqrt{5})$. في هذه الأمثلة، نحدد الشكل الحجري الحلبيرت-سايجل الأيجنستيم الذي يمكن أن يكون رفعا من الشكل الحجري الأيجنستيم.
In this paper we present an algorithm for computing Hecke eigensystems of Hilbert-Siegel cusp forms over real quadratic fields of narrow class number one. We give some illustrative examples using the quadratic field $Q(sqrt{5})$. In those examples, we identify Hilbert-Siegel eigenforms that are possible lifts from Hilbert eigenforms.
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