相关论文: Further properties of a function of Ogg and Ligoza…

Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of characteristic 0) and its nilpotent element e.…

Previous results on genera g of F_{q^2}-maximal curves are improved: (1) Either g\leq (q^2-q+4)/6, or g=\lfloor(q-1)^2/4\rfloor, or g=q(q-1)/2; (2) The hypothesis on the existence of a particular Weierstrass point in \cite{at} is proved;…

We show that many of Ramanujan's modular equations of degree 3 can be interpreted in terms of integral ternary quadratic forms. This way we establish that for any n in N |{n= x(x+1)/2 + y^2 +z^2 : x,y,z in Z}| >= |{n= x(x+1)/2 + 3y^2 +3z^2:…

Ramanujan famously found congruences for the partition function like p(5n+4) = 0 modulo 5. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on Gamma_{1}(4) which is…

Elliptic $K$-curves are elliptic curves defined over some field extension $L/K$ that are isogenous to all of their Galois conjugates. We present a new result on $K$-curves $E$ that are given by a $K$-rational orbit $\{\tau, -1/N\tau\}$ of…

The concept and the construction of modular graph functions are generalized from genus-one to higher genus surfaces. The integrand of the four-graviton superstring amplitude at genus-two provides a generating function for a special class of…

We study the quantum finite W-algebras W(gl_N,f), associated to the Lie algebra gl_N, and its arbitrary nilpotent element f. We construct for such an algebra an r_1 x r_1 matrix L(z) of Yangian type, where r_1 is the number of maximal parts…

We study very smooth functions on the real line, namely Schwartz functions, that satisfy a finite identity relating their translates and a single modulation. Concretely, we assume there is a nontrivial linear combination of translates of…

We give a classification of the degrees of the points with rational $j$-invariant on the modular curves $X_{0}(n)$ and $X_{1}(n)$. The degrees which occur infinitely often are computed unconditionally, while those which occur finitely often…

Fix a finite-dimensional simple Lie algebra $\mathfrak{g}$ and let $\mathfrak{g}_J\subseteq\mathfrak{g}$ be a Lie subalgebra coming from a Dynkin diagram inclusion. Then, the corresponding restriction functor is not essentially surjective…

In this paper we consider the algebra of upper triangular matrices UT$_n(F)$, endowed with a $\mathbb{Z}_2$-grading (superalgebra) and equipped with a superinvolution. These structures naturally arise in the context of Lie and Jordan…

It is well known that a Lipschitz function on the real line does not have to be operator Lipschitz. We show that the situation changes dramatically if we pass to H\"older classes. Namely, we prove that if $f$ belongs to the H\"older class…

We compute the divisor of the modular equation on the modular curve $\Gamma_0(N) \backslash \mathbb H^*$ and then find recurrence relations satisfied by the modular traces of the Hauptmodul for any congruence subgroup $\Gamma_0(N)$ of genus…

For some positive integers $g$ and $n$ we consider a subgroup $\mathbb{G}_{g,n}$ of the $2g$-dimensional modular group keeping invariant a certain locus $\mathcal{W}_{g,n}$ in the Siegel upper half plane of degree $g$. We address the…

The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_{\Omega}(G(|\nabla u|)+qF(u^+)+hu+\lambda_{+}\chi_{\{u>0\}} )\text{d}x\rightarrow\text{min}, \end{align*} in the class of functions…

We considerably improve Ono's and Ahlgren-Ono's work on the frequent occurrence of Ramanujan-type congruences for the partition function, and demonstrate that Ramanujan-type congruences occur in families that are governed by square-classes.…

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q=-1. This allows us to define graded modules over the Hecke algebra at q=-1…

The hypergeometric functions ${}_nF_{n-1}$ are higher transcendental functions, but for certain parameter values they become algebraic, because the monodromy of the defining hypergeometric differential equation becomes finite. It is shown…

Fix a prime N, and consider the action of the Hecke operator T_N on the space M_k(SL(2,Z)) of modular forms of full level and varying weight k. The coefficients of the matrix of T_N with respect to the basis {E_4^i E_6^j | 4i + 6j = k} for…

We describe an algorithm to compute the number of points over finite fields on a broad class of modular curves: we consider quotients $X_H/W$ for $H$ a subgroup of $\GL_2(\mathbb Z/n\mathbb Z)$ such that for each prime $p$ dividing $n$, the…