Irreducibility of Galois Actions on Level 1 Siegel Cusp Forms

2004 ◽  
pp. 75-80
Author(s):  
Luis V. Dieulefait
Keyword(s):  
Cusp Forms ◽  
Level 1 ◽  
Galois Actions

scholarly journals Products of vector valued Eisenstein series

2017 ◽  
Vol 29 (1) ◽  
Author(s):  
Martin Westerholt-Raum
Keyword(s):  
Eisenstein Series ◽  
Modular Forms ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Congruence Subgroups ◽  
Level 1 ◽  
Vector Valued ◽  
Level Aspect

AbstractWe prove that products of at most two vector valued Eisenstein series that originate in level 1 span all spaces of cusp forms for congruence subgroups. This can be viewed as an analogue in the level aspect to a result that goes back to Rankin, and Kohnen and Zagier, which focuses on the weight aspect. The main feature of the proof are vector valued Hecke operators. We recover several classical constructions from them, including classical Hecke operators, Atkin–Lehner involutions, and oldforms. As a corollary to our main theorem, we obtain a vanishing condition for modular forms reminiscent of period relations deduced by Kohnen and Zagier in the context their previously mentioned result.

scholarly journals ON REPRESENTATION OF MODULAR FORMS AS HOMOGENEOUS POLYNOMIALS

2017 ◽  
Vol 21 (6) ◽  
pp. 40-49
Author(s):  
G.V. Voskresenskaya
Keyword(s):  
Modular Forms ◽  
Homogeneous Polynomial ◽  
Cusp Forms ◽  
Homogeneous Polynomials ◽  
Base Functions ◽  
Level 1 ◽  
Eta Products

In the article we study the spaces of modular forms such that each element of them is a homogeneous polynomial of modular forms of low weights of the same level. It is a classical fact that it is true for the level 1. N. Koblitz point out that it is true for cusp forms of level 4. In this article we show that the analogous situation takes place for the levels corresponding to the eta-products with multiplicative coefficients. In all cases under consideration the base functions are eta-products. In each case the base functions are written explicitly. Dimensions of spaces are calculated by the Cohen - Oesterle formula, the orders in cusps are calculated by the Biagioli formula.

Polynomials for projective representations of level one forms

2011 ◽  
Author(s):  
Johan Bosman
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Cusp Forms ◽  
Tau Function ◽  
Projective Representations ◽  
Level 1

This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to 22. The chapter presents the result in terms of polynomials associated with the projectivized representations. As an application, it will improve a known result on Lehmer's nonvanishing conjecture for Ramanujan's tau function.

LINEAR CONGRUENCES AND RELATIONS ON SPACES OF CUSP FORMS

2007 ◽  
Vol 03 (04) ◽  
pp. 529-539 ◽  
Author(s):  
AHMAD EL-GUINDY
Keyword(s):  
Prime Ideal ◽  
Cusp Form ◽  
Modular Forms ◽  
Cusp Forms ◽  
Linear Combinations ◽  
Congruence Modulo ◽  
Hecke Eigenform ◽  
Modulo P ◽  
Linear Congruences ◽  
Level 1

Let p be a prime and let f be any cusp form of level l ∈ {2,3,5,7,13} whose weight satisfy a certain congruence modulo (p-1). Then we exhibit explicit linear combinations of the coefficients of f that must be divisible by p. For a normalized Hecke eigenform, this translates (under mild restrictions) into the pth coefficient itself being divisible by a prime ideal above p in the ring generated by the coefficients of f. This provides many instances of the so-called non-ordinary primes. We also discuss linear relations satisfied universally on the space of modular forms of these levels. These results extend recent work of Choie, Kohnen and Ono in the level 1 case.

Ultrastructural study on the development of rat amygdaloid body

1990 ◽  
Vol 48 (3) ◽  
pp. 432-433
Author(s):  
A. Manolova ◽  
S. Manolov
Keyword(s):  
Nerve Cells ◽  
Amygdaloid Complex ◽  
Amygdaloid Body ◽  
Thin Ring ◽  
Morphological Criteria ◽  
Neural Processes ◽  
Abundant Cytoplasm ◽  
Level 1 ◽  
Few Data ◽  
Oval Shape

Relatively few data on the development of the amygdaloid complex are available only at the light microscopic level (1-3). The existence of just general morphological criteria requires the performance of other investigations in particular ultrastructural in order to obtain new and more detailed information about the changes in the amygdaloid complex during development.The prenatal and postnatal development of rat amygdaloid complex beginning from the 12th embrionic day (ED) till the 33rd postnatal day (PD) has been studied. During the early stages of neurogenesis (12ED), the nerve cells were observed to be closely packed, small-sized, with oval shape. A thin ring of cytoplasm surrounded their large nuclei, their nucleoli being very active with various size and form (Fig.1). Some cells possessed more abundant cytoplasm. The perikarya were extremely rich in free ribosomes. Single sacs of the rough endoplasmic reticulum and mitochondria were observed among them. The mitochondria were with light matrix and possessed few cristae. Neural processes were viewed to sprout from some nerve cells (Fig.2). Later the nuclei were still comparatively large and with various shape.

Outcome der Geburtseinleitungen in einem Perinatalzentrum Level 1 in Bayern

2011 ◽  
Vol 215 (S 01) ◽  
Author(s):  
S Fürst ◽  
M Delius ◽  
F Karambiri ◽  
D Jacoby ◽  
U Hasbargen
Keyword(s):  
Level 1

Die intraartikuläre Therapie der Arthrose mit Hyaluronsäure – Stellenwert 2007

2007 ◽  
Vol 27 (04) ◽  
pp. 225-231
Author(s):  
Ingo Arnold
Keyword(s):  
Ex Vivo ◽  
Level 1

ZusammenfassungDie epidemiologischen Daten unterstreichen die Bedeutung derArthrosekrankheit. Obwohl in den letztenJahren erheb- licheAnstrengungenin immunologischerund pathophysio- logischer Hinsicht unternommen wurden, steht eine zufriedenstellende konservative Behandlungsoption weiterhin aus. Anders als in der internistischen Rheumatologie, wie am Beispiel der Biologicals ersichtlich, fehlt dem Orthopäden im Fall der Arthrose eine zuverlässige Möglichkeit, den Krankheitsverlauf nachhaltig zu beeinflussen. Arthrotische Gelenke zeigen u. a. eine deutlich erniedrigte Hyaluronan- Konzentration. Neben der Möglichkeit derVerbesserung der viskoelastischen Eigenschaften sind inzwischen auch zahlreiche immunmodulatorische Mechanismen im Zusammenhang mit der Gelenkhomöostase unter dem Einfluss von Hyaluronan (überwiegend ex vivo) nachgewiesen. Trotzdem ist unter Berücksichtigung einer umfassenden Übersicht über die zahlreichen Publikationen zu diesem Thema im Sinne eines Evidenzgrades Level 1 eher nur ein moderater Effektfür die allerdings risikoarme intra-artiku- läre Hyaluronan-Therapie abzuleiten. Für eine valide Aussage im direkten Vergleich mit i.a.-Kortikosteroid reicht dagegen die aktuelle Datenlage nicht aus.

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