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101.
Shinji Fukuhara Noriko Yui 《Transactions of the American Mathematical Society》2004,356(10):4237-4254
We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).
102.
103.
Matvei Libine 《Journal of Functional Analysis》2003,203(1):197-236
This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by Schmid (in: Deformation Theory and Symplectic Geometry, Mathematical Physics Studies, Vol. 20, Kluwer Academic Publishers, Dordrecht, 1997, pp. 259-270).A corresponding problem in the compact group setting was solved by Berline et al. (Heat Kernels and Dirac Operators, Springer, Berlin, 1992) by an application of the theory of equivariant forms and particularly the fixed point integral localization formula. This article (besides its representation-theoretical significance) provides a whole family of examples where it is possible to localize integrals to fixed points with respect to an action of a noncompact group. Moreover, a localization argument given here is not specific to the particular setting considered in this article and can be extended to a more general situation.There is a broadly accessible article (Libine, A Localization Argument for Characters of Reductive Lie Groups: An Introduction and Examples, 2002, math.RT/0208024) which explains how the argument works in the case, where the key ideas are not obstructed by technical details and where it becomes clear how it extends to the general case. 相似文献
104.
We consider quadratic diophantine equations of the shape
for a polynomial Q(X1, ..., Xs) Z[X1, ..., Xs] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s 3, the existence of a polynomialbound s(H) with the following property: if equation (1) hasa solution x Zs at all, then it has one satisfying
For s = 3 and s = 4 no polynomial bounds s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55. 相似文献
105.
Francesco?L.?ChieraEmail author 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2003,73(1):145-166
We consider the action of suitable trace operators on non homogeneous theta series that are Siegel modular forms for the principal
congruence subgroups of the symplectic group of odd levelq: Г
n
[q]. This is used for investigating whether modular forms forГ
n
[N], withN|q, which are linear combination of such theta series, can be expressed as combination of theta series that are modular forms
with respect toГ
n
[N]. 相似文献
106.
Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C
0
-semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity
assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions.
RID="h1"
ID="h1"Dédié à Philippe Bénilan
RID="*"
ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme". 相似文献
107.
In [9] we introduced the notion of equilibrium surface current JdSx on the closed C smooth surfaces in R
3 as a generalization of electric solenoid, and proved their existence. We here show an algorithm for JdSx starting from a given surface current J dSx on . 相似文献
108.
It is shown that the residue expansion of an elliptic Selberg integral gives rise to an integral representation for a multiple modular hypergeometric series. A conjectural evaluation formula for the integral then implies a closed summation formula for the series, generalizing both the multiple basic hypergeometric 87 sum of Milne-Gustafson type and the (one-dimensional) modular hypergeometric 87 sum of Frenkel and Turaev. Independently, the modular invariance ensures the asymptotic correctness of our multiple modular hypergeometric summation formula for low orders in a modular parameter. 相似文献
109.
Florian Luca. 《Mathematics of Computation》2001,70(234):893-896
For any , let be the th prime number. In this paper, we confirm a conjecture of Erdos and Stewart concerning all the solutions of the diophantine equation , when .
110.
Another Note on the Greatest Prime Factors of Fermat Numbers 总被引:1,自引:0,他引:1
For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the mth Fermat number, then P(Fm) 2m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and m a18.AMS Subject Classification (1991) 11A51 11J86 相似文献