Related papers: Selberg Formula for Cofinite Groups and the Roelke…
To any non-negatively graded dg Lie algebra $g$ over a field $k$ of characteristic zero we assign a functor $\Sigma_g: art/k \to Kan$ from the category of commutative local artinian $k$-algebras with the residue field $k$ to the category of…
This paper has been withdrawn by the author because there is a gap in Lemma 9.
This paper has been withdrawn by the author, due to a crucial error in page 5.
This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.
We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $G$ over a global function field is one less than the sum of the local ranks of $G$ taken over the places…
The purpose of this article is to prove that Gersten's conjecture for a commutative regular local ring is true. As its applications, we will prove the vanishing conjecture for certain Chow groups, generator conjecture for certain $K$-groups…
The paper is withdrawn by the author because it is superseded by cond-mat/0303357 .
In any positive genus case, we show an explicit formula of the Mumford forms expressed by infinite products like Selberg type zeta values for Schottky groups. This result is considered as an extension of the formula in terms of Ramanujan's…
This paper was withdrawn at the recommendation of the Cassini Radio Science Team.
This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…
As a generalization of the results [KW3],we study the functional equation of the higher Selberg zeta function for congruence subgroups. To obtain the gamma factor of this function, we introduce a higher Dirichlet $L$-function. Then we…
This paper has been withdrawn by the authors
General relativity cannot be formulated as a perturbatively renormalizable quantum field theory. An argument relying on the validity of the Bekenstein-Hawking entropy formula aims at dismissing gravity as non-renormalizable per se, against…
This paper has been withdrawn by the authors, due to the requirement of the Journal where a modified version will be published.
Let $G$ be a connected semisimple Lie group with finite center. Let $\Gamma \subset G$ be a discrete subgroup. We study closed admissible irreducible subrepresentations of the space of distributions $\mathcal S(\Gamma \backslash G)'$…
This paper has been withdrawn by the author(s), because it contains erroneous conclusion. Some part of the contents of the paper may be used in a future communication.
In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.
We formulate and prove a new variant of the Segal Conjecture describing the group of homotopy classes of stable maps from the p-completed classifying space of a finite group G to the classifying space of a compact Lie group K as the p-adic…
This paper has been withdrawn by the authors due to need of essential revision.
The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.