Related papers: Langlands' lambda function for quadratic tamely ra…

We prove three theorems concerning the Hopf-Galois module structure of fractional ideals in a finite tamely ramified extension of $ p $-adic fields or number fields which is $ H $-Galois for a commutative Hopf algebra $ H $. Firstly, we…

This paper provides some statistics for the coefficients of Russell- Type modular equations for the modular function, {\lambda}({\tau}). The results hold uniformly for all odd primes. They do not rely on any numerical evaluations of…

Let F be a totally real Galois number field. We prove the existence of base change relative to the extension F/Q for every classical newform of odd level, under simple local assumptions on the field F.

We compute asymptotic formulae for the mollified first and second moments for the family of quadratic Dirichlet $L$-functions in the function field setting. As an application, we obtain non-vanishing results for the derivatives of the…

In this paper we give the complete characterization of the boundedness of the generalized fractional maximal operator $$ M_{\phi,\Lambda^{\alpha}(b)}f(x) : = \sup_{Q \ni x} \frac{\|f \chi_Q\|_{\Lambda^{\alpha}(b)}}{\phi (|Q|)} \qquad (x \in…

Let K be a local field of characteristic p with perfect residue field k. In this paper we find a set of representatives for the k-isomorphism classes of totally ramified separable extensions L/K of degree p. This extends work of Klopsch,…

Coefficients in the expansions of the form $\partial P_{n}(\lambda;z)}/\partial\lambda=\sum_{k=0}^{n}a_{nk}(\lambda)P_{k}(\lambda;z)$, where $P_{n}(\lambda;z)$ is the $n$th classical (the generalized Laguerre, Gegenbauer or Jacobi)…

We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number…

In this paper we associate an invariant to a biquaternion algebra $B$ over a field $K$ with a subfield $F$ such that $K/F$ is a quadratic separable extension and $\operatorname{char}(F)=2$. We show that this invariant is trivial exactly…

Low-temperature expansion of the effective Lagrangian of the QED$_{3+1}$ with a uniform magnetic field and a finite chemical potential is performed. Temperature corrections, as well as zero-temperature expression for the effective…

Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$…

We show that a strongly $\lambda$-spirallike function of order $\alpha$ can be extended to a $\sin(\pi\alpha/2)$-quasiconformal automorphism of the complex plane for $-\pi/2<\lambda<\pi/2$ and $0<\alpha<1$ with $|\lambda|<\pi\alpha/2.$ In…

Given a field K, a quadratic extension field L is an extension of K that can be generated from K by adding a root of a quadratic polynomial with coefficients in K. This paper shows how ACL2(r) can be used to reason about chains of quadratic…

This paper refers to Langlands' big set of notes [L] devoted to the question if the (normalized) local Hecke-Tate root number $\Delta=\Delta(E,\chi)$, where $E$ is a finite separable extension of a fixed non-archimedean local field $F$, and…

In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…

Cyclic, ramified extensions $L/K$ of degree $p$ of local fields with residue characteristic $p$ are fairly well understood. Unless $\mbox{char}(K)=0$ and $L=K(\sqrt[p]{\pi_K})$ for some prime element $\pi_K\in K$, they are defined by an…

We study the following question: given a global field $F$ and finite group $G$, what is the minimal $r$ such that there exists a finite extension $K/F$ with $\mathrm{Aut}(K/F)\cong G$ that is ramified over exactly $r$ places of $F$? We…

Let $K:k$ be a field extension and let $\Lambda$ be a finite-dimensional $k$-algebra. We investigate the relationship between $\Lambda$ and $\Lambda_K = \Lambda \otimes_k K$ with particular emphasis on various aspects of $\tau$-tilting…

We construct a Langlands parameterization of supercuspidal representations of $G_2$ over a $p$-adic field. More precisely, for any finite extension $K / \QQ_p$ we will construct a bijection \[ \CL_g : \CA^0_g(G_2,K) \rightarrow \CG^0(G_2,K)…

We prove that every place of an algebraic function field F|K of arbitrary characteristic admits local uniformization in a finite extension F' of F. We show that F'|F can be chosen to be normal. If K is perfect and P is of rank 1, then…