1.
Zeta and $L$-functions and Bernoulli polynomials of root systems - Komori, Yasushi; Matsumoto, Kohji; Tsumura, Hirofumi
This article is essentially an announcement of the papers [7,8,9,10] of the authors, though some of the examples are not included in those papers. We consider what is called zeta and $L$-functions of root systems which can be regarded as a multi-variable version of Witten multiple zeta and $L$-functions. Furthermore, corresponding to these functions, Bernoulli polynomials of root systems are defined. First we state several analytic properties, such as analytic continuation and location of singularities of these functions. Secondly we generalize the Bernoulli polynomials and give some expressions of values of zeta and $L$-functions of root systems in terms of...
3.
A new class of nonassociative algebras with involution - Kamiya, Noriaki; Mondoc, Daniel
This article is devoted to introduce a new class of nonassociative algebras with involution including the class of structurable algebras.
4.
A remark on uniqueness theorems in an angular domain - Wu, Zhao-Jun; Sun, Dao-Chun
In this paper, we deal with the problem of uniqueness for meromorphic functions in the whole complex plane $\mathbf{C}$ under some shared-value/set conditions in an angular domain instead of the whole plane. Results are obtained extending some results by Lin, Mori and Tohge [W. C. Lin, S. Mori and K. Tohge, Uniqueness theorems in an angular domain, Tohoku Math. J., \textbf{58} (2006), 509527].
5.
Discreteness of subgroups of $PU(1,n;\mathbf{C})$ - Xie, BaoHua; Jiang, YuePing; Wang, Hua
In this paper, we discuss three discreteness criterions of $n$-dimensional subgroup $G$ of $PU(1,n;\mathbf{C})$. This generalize some discreteness criterions established by J. Gilman [3], S. Yang and A. Fang [9].
6.
A rationality problem of some Cremona transformation - Hoshi, Akinari; Kang, Ming-chang
In this note we give a new approach to the rationality problem of some Cremona transformation. Let $k$ be any field, $k(x,y)$ be the rational function field of two variables over $k$. Let $\sigma$ be a $k$-automorphism of $k(x,y)$ defined by
\begin{equation*}
\sigma(x) = \frac{-x(3x-9y-y^{2})^{3}}{(27x+2x^{2}+9xy+2xy^{2}-y^{3})^{2}},\quad \sigma(y) = \frac{-(3x+y^{2})(3x-9y-y^{2})}{27x+2x^{2}+9xy+2xy^{2}-y^{3}}.
\end{equation*}
Theorem. The fixed field $k(x,y)^{\langle\sigma\rangle}$ is rational (= purely transcendental) over $k$. Embodied in a new proof of the above theorem are several general guidelines for solving the rationality problem of Cremona transformations, which may be applied elsewhere.
7.
Absolute zeta functions - Deitmar, Anton; Koyama, Shin-ya; Kurokawa, Nobushige
Two new concepts of zeta functions for schemes over the field of one element are proposed. A localization formula and an explicit formula in the affine case are given. This allows for a computation for every scheme.
8.
Generic Torelli theorem for quintic-mirror family - Usui, Sampei
This article is a geometric application of polarized logarithmic Hodge theory of Kazuya Kato and Sampei Usui. We prove generic Torelli theorem for the well-known quintic-mirror family in two ways by using different logarithmic points at the boundary of the fine moduli of polarized logarithmic Hodge structures.
9.
The number of modular extensions of odd degree of a local field - Yamagishi, Masakazu
The number of Galois extensions, up to isomorphism, of a local field whose Galois groups are isomorphic to the modular group $M_{p^{m}}=\langle x,y\mid x^{p^{m-1}}=y^{p}=1,y^{-1}xy=x^{p^{m-2}+1}\rangle$, where $p$ is an odd prime, is counted.
10.
Modular relation interpretation of the series involving
the Riemann zeta values - Li, Hai-Long; Kanemitsu, Shigeru; Tsukada, Haruo
We shall locate Katsuradas results, in our framework of modular relations, on two series involving the values of the Riemann zeta-function, which are decisive generalizations of earleir results of Chowla and Hawkins and of Buschman and Srivastava \textit{et al.} We shall elucidate these results as an improper or a proper modular relation according as the involved parameter $\nu$ exerts effects on the series or not, eventually indicating that they are disguised form of modular relations as given by Theorem 4 in 3.
12.
On the maximal signless Laplacian spectral radius of graphs with given matching number - Yu, Guihai
Let $\mathcal{G}_{n,\beta}$ be the set of simple graphs of order $n$ with given matching number $\beta$. In this paper, we investigate the maximal signless Laplacian spectral radius in $\mathcal{G}_{n,\beta}$ and characterize the extremal graphs with maximal signless Laplacian spectral radius.
13.
Extension of the Beurlings Theorem - Yousefi, Bahmann; Hesameddini, Esmaiel
Under some conditions on a Hilbert space $H$ of analytic functions on the open unit disc we will show that for every nontrivial invariant subspace $\mathcal{M}$ of $H$, there exists a unique nonconstant inner function $\varphi$ such that $\mathcal{M}=\varphi H$. This extends the Beurlings Theorem.
14.
Trace formula and trace identity of twisted Hecke operators on the spaces of cusp forms of weight $k+1/2$ and level $32M$ - Ueda, Masaru
Let $M$ be an odd positive integer, $\chi$ an even quadratic character defined modulo $32 M$, and $\psi$ a quadratic primitive character of conductor divisible by 8. Then, we can define twisted Hecke operators $R_{\psi} \tilde{T}(n^{2})$ on the space of cusp forms of weight $k+1/2$, level $32M$, and character $\chi$, under certain conditions on the conductors of $\chi$ and $\psi$. This is a specific feature of the case of half-integral weight. We give explicit trace formulas of the twisted Hecke operators and their trace identities.
15.
Notes to the Feit-Thompson conjecture - Motose, Kaoru
We shall present partial solutions to the conjecture such that $(q^{p}-1)/(q-1)$ does not divide $(p^{q}-1)/(p-1)$ for distinct primes $p < q$.
16.
On the inviscid Proudman-Johnson equation - Constantin, Adrian; Wunsch, Marcus
We show that certain qualitative properties of classical solutions to the inviscid Proudman-Johnson equation are preserved as long as these solutions exist. This enables us to give a simple blow-up criterion.
17.
Growth functions for Artin monoids - Saito, Kyoji
In [S1], we showed that the growth function $P_M(t)$ for an Artin monoid associated with a Coxeter matrix $M$ of finite type is a rational function of the form $1/(1 - t)N_M(t)$, where $N_M(t)$ is a polynomial determined by the Coxeter-Dynkin graph for $M$, and is called the denominator polynomial of type $M$. We formulated three conjectures on the zeros of the denominator polynomial. In the present note, we prove that the same denominator formula holds for an arbitrary Artin monoid, and formulate slightly modified conjectures on the zeros of the denominator polynomials of affine types. The new conjectures are...
19.
On injectivity, vanishing and torsion-free theorems for algebraic varieties - Fujino, Osamu
We give a short and almost self-contained proof of generalizations of Kollár’s vanishing and torsion-free theorems. Although they are contained in Ambro's much more general results on embedded normal crossing pairs, we give an alternate and direct reduction argument to the mixed Hodge theory. In this sense, this paper gives a more readable account of the application to the log minimal model program for log canonical pairs.
20.
On the critical case of Okamoto’s continuous non-differentiable functions - Kobayashi, Kenta
In a recent paper in this Proceedings, H. Okamoto presented a parameterized family of continuous functions which contains Bourbaki’s and Perkins’s nowhere differentiable functions as well as the Cantor-Lebesgue singular function. He showed that the function changes it’s differentiability from ‘differentiable almost everywhere’ to ‘non-differentiable almost everywhere’ at a certain parameter value. However, differentiability of the function at the critical parameter value remained unknown. For this problem, we prove that the function is non-differentiable almost everywhere at the critical case.
1.
