scholarly journals The parallelogram identity on groups and deformations of the trivial character in $\protect \mathrm{SL}_2(\protect \mathbb{C})$

2020 ◽  
Vol 7 ◽  
pp. 263-285
Author(s):  
Julien Marché ◽  
Maxime Wolff
Keyword(s):  
Trivial Character

scholarly journals CONSTRUCTING SIMULTANEOUS HECKE EIGENFORMS

2010 ◽  
Vol 06 (05) ◽  
pp. 1117-1137 ◽  
Author(s):  
T. SHEMANSKE ◽  
S. TRENEER ◽  
L. WALLING
Keyword(s):  
Hecke Operators ◽  
Cusp Forms ◽  
Hecke Eigenforms ◽  
Linearly Independent ◽  
Integral Weight ◽  
Trivial Character ◽  
Free Level ◽  
Fixed Space ◽  
Space Of Cusp Forms

It is well known that newforms of integral weight are simultaneous eigenforms for all the Hecke operators, and that the converse is not true. In this paper, we give a characterization of all simultaneous Hecke eigenforms associated to a given newform, and provide several applications. These include determining the number of linearly independent simultaneous eigenforms in a fixed space which correspond to a given newform, and characterizing several situations in which the full space of cusp forms is spanned by a basis consisting of such eigenforms. Part of our results can be seen as a generalization of results of Choie–Kohnen who considered diagonalization of "bad" Hecke operators on spaces with square-free level and trivial character. Of independent interest, but used herein, is a lower bound for the dimension of the space of newforms with arbitrary character.

scholarly journals THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS

2015 ◽  
Vol 3 ◽  
Author(s):  
XIN WAN
Keyword(s):  
Modular Forms ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Selmer Group ◽  
Hilbert Modular Form ◽  
Main Conjecture ◽  
Hilbert Modular ◽  
Trivial Character ◽  
The One ◽  
Ordinary Reduction

Following the ideas and methods of a recent work of Skinner and Urban, we prove the one divisibility of the Iwasawa main conjecture for nearly ordinary Hilbert modular forms under certain local hypotheses. As a consequence, we prove that for a Hilbert modular form of parallel weight, trivial character, and good ordinary reduction at all primes dividing$p$, if the central critical$L$-value is zero then the$p$-adic Selmer group of it has rank at least one. We also prove that one of the local assumptions in the main result of Skinner and Urban can be removed by a base-change trick.

Heights and L-Series

1990 ◽  
Vol 42 (3) ◽  
pp. 533-560 ◽  
Author(s):  
Rhonda Lee Hatcher
Keyword(s):  
Dirichlet Series ◽  
Cusp Form ◽  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Ideal Class ◽  
Quadratic Character ◽  
Trivial Character ◽  
Image Position

Let be a cusp form of weight 2k and trivial character for Γ0(N), where N is prime, which is orthogonal with respect to the Petersson product to all forms g(dz), where g is of level L < N, dL\N. Let K be an imaginary quadratic field of discriminant — D where the prime N is inert. Denote by ∊ the quadratic character of determined by ∊(p) = (—D/p) for primes p not dividing D. For A an ideal class in K, let rA(m) be the number of integral ideals of norm m in A. We will be interested in the Dirichlet series L(f,A,s) defined by

scholarly journals THE HOLOMORPHY CONJECTURE FOR NONDEGENERATE SURFACE SINGULARITIES

2016 ◽  
Vol 227 ◽  
pp. 160-188
Author(s):  
WOUTER CASTRYCK ◽  
DENIS IBADULA ◽  
ANN LEMAHIEU
Keyword(s):  
Zeta Function ◽  
Arbitrary Dimension ◽  
Newton Polyhedron ◽  
Character Sums ◽  
Specific Character ◽  
Trivial Character ◽  
Surface Singularities ◽  
Local Monodromy

The holomorphy conjecture roughly states that Igusa’s zeta function associated to a hypersurface and a character is holomorphic on$\mathbb{C}$whenever the order of the character does not divide the order of any eigenvalue of the local monodromy of the hypersurface. In this article, we prove the holomorphy conjecture for surface singularities that are nondegenerate over$\mathbb{C}$with respect to their Newton polyhedron. In order to provide relevant eigenvalues of monodromy, we first show a relation between the normalized volumes (which appear in the formula of Varchenko for the zeta function of monodromy) of the faces in a simplex in arbitrary dimension. We then study some specific character sums that show up when dealing with false poles. In contrast to the context of the trivial character, we here need to show fakeness of certain candidate poles other than those contributed by$B_{1}$-facets.

scholarly journals La regionalización de la educación como tecnología cognitiva virtual

10.14201/3123 ◽  
2009 ◽  
Vol 9 ◽  
Author(s):  
Antoni J. Colom Cañellas
Keyword(s):  
Knowledge Acquisition ◽  
Right Hemisphere ◽  
New Technology ◽  
Cognitive Technology ◽  
Theory Of Education ◽  
Trivial Character ◽  
Nuevas Tecnologías ◽  
Systemic Thought ◽  
The Right ◽  
The Brain

RESUMEN: La influencia de las nuevas tecnologías en la educación nos obliga a una redefinición conceptual de la misma. Tras analizar los efectos de la virtualidad en el campo de la educación, de la escuela y de los sujetos, se concibe la Teoría de la Educación como una tecnología cognitiva de carácter no trivial. Sólo así se plantea una educación para la innovación del conocimiento capaz de contemplar la creatividad y con ella las atribuciones propias del pensamiento sistémico. Además se confirman estas tesis con las últimas investigaciones de la neurociencia referidas al hemisferio cerebral derecho.ABSTRACT: The influence of new technology on education brings with it the necessity of a conceptual redefinition of the term. After analyzing the effects of virtuality in the field of education, in the school, and on the individuáis, we can conceive the Theory of Education as a cognitive technology of no trivial character. Only in this way can we design an education for the innovation of knowledge acquisition capable of contemplating creativity and along with in the attributions characteristic of systemic thought. Furthermore, these theses are being confirmed by the latest findings in neuroscience referring to the right hemisphere of the brain.

scholarly journals Linear Models: A Useful “Microscope” for Causal Analysis

2013 ◽  
Vol 1 (1) ◽  
pp. 155-170 ◽  
Author(s):  
Judea Pearl
Keyword(s):  
Selection Bias ◽  
Measurement Errors ◽  
Linear Models ◽  
Causal Analysis ◽  
Case Control ◽  
Linear Path ◽  
Trivial Character ◽  
Reverse Regression ◽  
Bias Selection ◽  
Collider Bias

AbstractThis note reviews basic techniques of linear path analysis and demonstrates, using simple examples, how causal phenomena of non-trivial character can be understood, exemplified and analyzed using diagrams and a few algebraic steps. The techniques allow for swift assessment of how various features of the model impact the phenomenon under investigation. This includes: Simpson’s paradox, case–control bias, selection bias, missing data, collider bias, reverse regression, bias amplification, near instruments, and measurement errors.

The Residual Spectrum of G2

1996 ◽  
Vol 48 (6) ◽  
pp. 1245-1272 ◽  
Author(s):  
Henry H. Kim
Keyword(s):  
Maximal Torus ◽  
Exceptional Group ◽  
Residual Spectrum ◽  
Component Group ◽  
Trivial Character

AbstractWe completely determine the residual spectrum of the split exceptional group of type G2, thus completing the work of Langlands and Moeglin-Waldspurger on the part of the residual spectrum attached to the trivial character of the maximal torus. We also give the Arthur parameters for the residual spectrum coming from Borel subgroups. The interpretation in terms of Arthur parameters explains the “bizarre” multiplicity condition in Moeglin-Waldspurger's work. It is related to the fact that the component group of the Arthur parameter is non-abelian.

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