Displaying similar documents to “On the angles between certain arithmetically defined subspaces of 𝐂 n

Generalized symmetry classes of tensors

Gholamreza Rafatneshan, Yousef Zamani (2020)

Czechoslovak Mathematical Journal

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Let V be a unitary space. For an arbitrary subgroup G of the full symmetric group S m and an arbitrary irreducible unitary representation Λ of G , we study the generalized symmetry class of tensors over V associated with G and Λ . Some important properties of this vector space are investigated.

L p , q spaces

Joseph Kupka

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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the L p , q spaces................................. 114. Integral representation of bounded linear functionals on L p , q ( B ) ........ 235. Examples in L p , q theory...................................................................................

A new characterization for the simple group PSL ( 2 , p 2 ) by order and some character degrees

Behrooz Khosravi, Behnam Khosravi, Bahman Khosravi, Zahra Momen (2015)

Czechoslovak Mathematical Journal

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Let G be a finite group and p a prime number. We prove that if G is a finite group of order | PSL ( 2 , p 2 ) | such that G has an irreducible character of degree p 2 and we know that G has no irreducible character θ such that 2 p θ ( 1 ) , then G is isomorphic to PSL ( 2 , p 2 ) . As a consequence of our result we prove that PSL ( 2 , p 2 ) is uniquely determined by the structure of its complex group algebra.

On the higher power moments of cusp form coefficients over sums of two squares

Guodong Hua (2022)

Czechoslovak Mathematical Journal

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Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = SL ( 2 , ) . Denote by λ f ( n ) the n th normalized Fourier coefficient of f . We are interested in the average behaviour of the sum a 2 + b 2 x λ f j ( a 2 + b 2 ) for x 1 , where a , b and j 9 is any fixed positive integer. In a similar manner, we also establish analogous results for the normalized coefficients of Dirichlet expansions of associated symmetric power L -functions and Rankin-Selberg L -functions.

Lower bounds for the largest eigenvalue of the gcd matrix on { 1 , 2 , , n }

Jorma K. Merikoski (2016)

Czechoslovak Mathematical Journal

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Consider the n × n matrix with ( i , j ) ’th entry gcd ( i , j ) . Its largest eigenvalue λ n and sum of entries s n satisfy λ n > s n / n . Because s n cannot be expressed algebraically as a function of n , we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S. Hong, R. Loewy (2004). We also conjecture that λ n > 6 π - 2 n log n for all n . If n is large enough, this follows from F. Balatoni (1969).

Asymptotic values of modular multiplicities for GL 2

Sandra Rozensztajn (2014)

Journal de Théorie des Nombres de Bordeaux

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We study the irreducible constituents of the reduction modulo p of irreducible algebraic representations V of the group Res K / p GL 2 for K a finite extension of p . We show that asymptotically, the multiplicity of each constituent depends only on the dimension of V and the central character of its reduction modulo p . As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.

Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL 2 ( q ) for q 7

Mark L. Lewis, Yanjun Liu, Hung P. Tong-Viet (2018)

Czechoslovak Mathematical Journal

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Let G be a finite group and write cd ( G ) for the degree set of the complex irreducible characters of G . The group G is said to satisfy the two-prime hypothesis if for any distinct degrees a , b cd ( G ) , the total number of (not necessarily different) primes of the greatest common divisor gcd ( a , b ) is at most 2 . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL 2 ( q ) for q 7 .

On higher moments of Hecke eigenvalues attached to cusp forms

Guodong Hua (2022)

Czechoslovak Mathematical Journal

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Let f , g and h be three distinct primitive holomorphic cusp forms of even integral weights k 1 , k 2 and k 3 for the full modular group Γ = SL ( 2 , ) , respectively, and let λ f ( n ) , λ g ( n ) and λ h ( n ) denote the n th normalized Fourier coefficients of f , g and h , respectively. We consider the cancellations of sums related to arithmetic functions λ g ( n ) , λ h ( n ) twisted by λ f ( n ) and establish the following results: n x λ f ( n ) λ g ( n ) i λ h ( n ) j f , g , h , ε x 1 - 1 / 2 i + j + ε for any ε > 0 , where 1 i 2 , j 5 are any fixed positive integers.

On sharp characters of type { - 1 , 0 , 2 }

Alireza Abdollahi, Javad Bagherian, Mahdi Ebrahimi, Maryam Khatami, Zahra Shahbazi, Reza Sobhani (2022)

Czechoslovak Mathematical Journal

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For a complex character χ of a finite group G , it is known that the product sh ( χ ) = l L ( χ ) ( χ ( 1 ) - l ) is a multiple of | G | , where L ( χ ) is the image of χ on G - { 1 } . The character χ is said to be a sharp character of type L if L = L ( χ ) and sh ( χ ) = | G | . If the principal character of G is not an irreducible constituent of χ , then the character χ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups G with normalized sharp characters of type { - 1 , 0 , 2 } . Here we prove that such a group with nontrivial...

On Kakeya–Nikodym averages, L p -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions

Matthew D. Blair, Christopher D. Sogge (2015)

Journal of the European Mathematical Society

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We extend a result of the second author [27, Theorem 1.1] to dimensions d 3 which relates the size of L p -norms of eigenfunctions for 2 < p < 2 ( d + 1 ) / d - 1 to the amount of L 2 -mass in shrinking tubes about unit-length geodesics. The proof uses bilinear oscillatory integral estimates of Lee [22] and a variable coefficient variant of an " ϵ removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] L 2 oscillatory integral theorem and the Cartan–Hadamard theorem to show that, under the assumption of nonpositive...

Locally analytic vectors of unitary principal series of  GL 2 ( p )

Ruochuan Liu, Bingyong Xie, Yuancao Zhang (2012)

Annales scientifiques de l'École Normale Supérieure

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The p -adic local Langlands correspondence for  GL 2 ( p ) attaches to any 2 -dimensional irreducible p -adic representation V of  G p an admissible unitary representation Π ( V ) of  GL 2 ( p ) . The unitary principal series of  GL 2 ( p ) are those Π ( V ) corresponding to trianguline representations. In this article, for  p &gt; 2 , using the machinery of Colmez, we determine the space of locally analytic vectors Π ( V ) an for all non-exceptional unitary principal series Π ( V ) of  GL 2 ( p ) by proving a conjecture of Emerton.