Displaying similar documents to “Li coefficients for automorphic L -functions”

Special values of symmetric power L -functions and Hecke eigenvalues

Emmanuel Royer, Jie Wu (2007)

Journal de Théorie des Nombres de Bordeaux

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We compute the moments of L -functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the L -functions of modular forms. We show that, in the case of even powers, it is equivalent to twist by the value at the edge of the critical strip of the symmetric square L -functions. We deduce information on the size of symmetric power L -functions at the edge of the critical strip in subfamilies. In a second part, we study the distribution of...

Long time asymptotics of the Camassa–Holm equation on the half-line

Anne Boutet de Monvel, Dmitry Shepelsky (2009)

Annales de l’institut Fourier

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We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation u t - u t x x + 2 u x + 3 u u x = 2 u x u x x + u u x x x on the half-line x ≥ 0 . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane x > 0 , t > 0 having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of...

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón (2009)

Annales de l’institut Fourier

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The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at ℂ n ( n > 1 ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...

Higher regularizations of zeros of cuspidal automorphic L -functions of GL d

Masato Wakayama, Yoshinori Yamasaki (2011)

Journal de Théorie des Nombres de Bordeaux

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We establish “higher depth” analogues of regularized determinants due to Milnor for zeros of cuspidal automorphic L -functions of GL d over a general number field. This is a generalization of the result of Deninger about the regularized determinant for zeros of the Riemann zeta function.

On q -summation and confluence

Lucia Di Vizio, Changgui Zhang (2009)

Annales de l’institut Fourier

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This paper is divided in two parts. In the first part we study a convergent q -analog of the divergent Euler series, with q ∈ ( 0 , 1 ) , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding q -difference equation. In the second part, we work under the assumption q ∈ ( 1 , + ∞ ) . In this case, at least four different q -Borel sums of a divergent power series solution of an irregular...