Displaying similar documents to “New models for the action of Hecke operators in spaces of Maass wave forms”

On the generation of the coefficient field of a newform by a single Hecke eigenvalue

Koopa Tak-Lun Koo, William Stein, Gabor Wiese (2008)

Journal de Théorie des Nombres de Bordeaux

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Let f be a non-CM newform of weight k ≥ 2 . Let L be a subfield of the coefficient field of  f . We completely settle the question of the density of the set of primes p such that the p -th coefficient of  f generates the field  L . This density is determined by the inner twists of  f . As a particular case, we obtain that in the absence of nontrivial inner twists, the density is  1 for L equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which...

Exponential sums with coefficients 0 or 1 and concentrated L p norms

B. Anderson, J. M. Ash, R. L. Jones, D. G. Rider, B. Saffari (2007)

Annales de l’institut Fourier

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A sum of exponentials of the form f ( x ) = exp 2 π i N 1 x + exp 2 π i N 2 x + ⋯ + exp 2 π i N m x , where the N k are distinct integers is called an (because the convolution of f with itself is f ) or, simply, an . We show that for every p > 1 , and every set E of the torus 𝕋 = ℝ / ℤ with | E | > 0 , there are idempotents concentrated on E in the L p sense. More precisely, for each p > 1 , there is an constant C p > 0 so that for each E with | E | > 0 and ϵ > 0 one can find an idempotent f such that the ratio ∫ E | f | p / ∫ 𝕋 | f | p 1 / p is greater than C p - ϵ . This is in fact a lower bound result and, though optimal, it is close...

A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen (2006)

Annales de l’institut Fourier

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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F . We do this for automorphic representations of an arbitrary reductive group G over F , which is compact at infinity. In the special case where G is an inner form of GSp ( 4 ) over ℚ , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

Holomorphic retractions and boundary Berezin transforms

Jonathan Arazy, Miroslav Engliš, Wilhelm Kaup (2009)

Annales de l’institut Fourier

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In an earlier paper, the first two authors have shown that the convolution of a function f continuous on the closure of a Cartan domain and a K -invariant finite measure μ on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face F depends only on the restriction of f to F and is equal to the convolution, in  F , of the latter restriction with some measure μ F on F uniquely determined by  μ . In this article, we give an explicit formula for μ F in...

Shintani and Shimura lifts of cusp forms on certain arithmetic groups and their applications

SoYoung Choi, Chang Heon Kim (2017)

Open Mathematics

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For an odd and squarefree level N, Kohnen proved that there is a canonically defined subspace [...] S κ + 1 2 n e w ( N ) ⊂ S κ + 1 2 ( N ) , and S κ + 1 2 n e w ( N ) and S 2 k n e w ( N ) S κ + 1 2 n e w ( N ) ⊂ S κ + 1 2 ( N ) , and S κ + 1 2 n e w ( N ) and S 2 k n e w ( N ) are isomorphic as modules over the Hecke algebra. Later he gave a formula for the product [...] a g ( m ) a g ( n ) ¯ a g ( m ) a g ( n ) ¯ of two arbitrary Fourier coefficients of a Hecke eigenform g of halfintegral weight and of level 4N in terms of certain cycle integrals of the corresponding form f of integral...