772 research outputs found
Mathematical and Numerical Studies on Meshless Methods for Exterior Unbounded Domain Problems
The method of fundamental solution (MFS) is an efficient meshless method for
solving a boundary value problem in an exterior unbounded domain. The numerical
solution obtained by the MFS is accurate, while the corresponding matrix
equation is ill-conditioned. A modified MFS (MMFS) with the proper basis
functions is proposed by the introduction of the modified Trefftz method (MTM).
The concrete expressions of the corresponding condition numbers and the
solvability by these methods are mathematically proven. Thereby, the optimal
parameter minimizing the condition number is also mathematically given.
Numerical experiments show that the condition numbers of the matrices
corresponding to the MTM and the MMFS are reduced and that the numerical
solution by the MMFS is more accurate than the one by the conventional method.Comment: 25 pages, 11 figure
Koecher-Maass series of the Ikeda lift for U(m,m)
Let K be an imaginary quadratic field with discriminant -D, and x the
Dirichlet character corresponding to the extension K/Q. Let m=2n or 2n+1 with n
a positive integer. Let f be a primitive form of weight 2k+1 and level D with
Neben character x, or a primitive form of weight 2k for SL(2,Z) according as
m=2n, or m=2n+1. For such an f let I(m,f) be the lift of f to the space of
Hermitian modular forms of degree m constructed by Ikeda. We then give an
explicit formula of the Koecher-Maass series L(s,I(m,f)) of I(m,f). This is a
generalization of [Y. Mizuno, Manuscripta Math. 119(2006), 175-216].Comment: This paper will appear in Kyoto Journal of Mathematics. arXiv admin
note: substantial text overlap with arXiv:1102.439
Period of the adelic Ikeda lift for U(m, m)
We give a period formula for the adelic Ikeda lift of an elliptic modular form f for U(m, m) in terms of special values of the adjoint L-functions of f. This is an adelic version of Ikeda’s conjecture on the period of the classical Ikeda lift for U(m, m)
On the period of the Ikeda lift for U(m,m)
Let K be an imaginary quadratic field, and x the Dirichlet character
corresponding to the extension K/Q. Let m=2n or 2n+1 with n a positive integer.
Let f be a primitive form of weight 2k+1 and and nebentype x, or a primitive
form of weight 2k for SL(2,Z) according as m=2n, or m=2n+1. For such an f let
I_m(f) be the lift of f to the space of modular forms of weight 2k+2n for the
Hermitian modular group of degree m constructed by Ikeda.
We then express the period of I_m(f) in terms of special
values of the adjoint L-functions of f. This poves the conjecture concerning
the period of the Ikeda lift proposed by Ikeda.Comment: The version arXiv:1102.4393v2. is a shortened version of the paper
arXiv:1102.4393v1. Some results in arXiv:1102.4393v1 is proved in
arXiv:1403.2175v2. This is a revised version of arXiv:1102.4393v
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