Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and ...singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).
Let E/Q be a real quadratic field and π0 a cuspidal, irreducible, automorphic representation of GL(2,AE) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We ...show that there exists a non-zero Siegel paramodular newform F:H2→C with weight, level, Hecke eigenvalues, epsilon factor and L-function determined explicitly by π0. We tabulate these invariants in terms of those of π0 for every prime p of Q.
In this paper we consider the theta correspondence between the sets \operatorname{Irr} (\operatorname{GSp} (2,k)) and \operatorname{Irr} (\operatorname{GO} (X)) when k is a nonarchimedean local field ...and \dim _{k} X =4. Our main theorem determines all the elements of \operatorname{Irr} (\operatorname{GO} (X)) that occur in the correspondence. The answer involves distinguished representations. As a corollary, we characterize all the elements of \operatorname{Irr} (\operatorname{O} (X)) that occur in the theta correspondence between \operatorname{Irr} (\operatorname{Sp} (2,k)) and \operatorname{Irr} (\operatorname{O} (X)). We also apply our main result to prove a case of a new conjecture of S.S. Kudla concerning the first occurrence of a representation in the theta correspondence.
The assumptions educators possess about themselves, their role as teachers, and their students' capabilities play a significant role in determining expectations, teaching practices, and ultimately ...student happiness and success. This article provides an overview of the application of resilience principles in the classroom from the perspective of the mindset of effective educators. In their efforts to nurture resilience in their students, effective educators appreciate the life-long impact they have on students, acknowledge that all students want to be successful, and appreciate that the foundation for successful learning in a safe and secure classroom climate is the relationship they forge with students. Ideas and strategies are offered to assist teachers in developing a mindset capable of fostering resilience in students.
Les suppositions qu'ont les enseignants par rapport à eux-mêmes, à leur rôle et aux capacités de leurs étudiants jouent un rôle significatif quant à leurs attentes, à leurs façons d'enseigner et, en bout de ligne, au bonheur et au succès des étudiants. Cet article donne une vue d'ensemble de l'application des principes de résilience dans la classe en adoptant la perspective fournie par l'état d'esprit d'éducateurs efficaces. Dans leurs efforts pour entretenir la résilience, les enseignants efficaces sont conscients de l'effet durable qu'ils ont sur leurs étudiants, ils reconnaissent que tous veulent réussir et ils se rendent comptent que la base d'un apprentissage réussi dans un climat sûr passe par la relation qu'ils forgent avec eux. On y présente également des idées et des stratégies pour aider les enseignants à développer un état d'esprit capable d'engendrer la résilience chez les étudiants.
We give a presentation via generators and relations of the local graded paramodular Hecke algebra of prime level. In particular, we prove that the paramodular Hecke algebra is isomorphic to the ...quotient of the free \(\mathbb{Z}\)-algebra generated by four non-commuting variables by an ideal generated by seven relations. Using this description, we derive rationality results at the level of characters and give a characterization of the center of the Hecke algebra. Underlying our results are explicit formulas for the product of any generator with any double coset.
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