Zobrazeno 1 - 10
of 163
pro vyhledávání: '"Goldfeld, Dorian"'
Let $\Phi_1,\Phi_2$ be Maass forms for $\text{SL}(2,\mathbb Z)$ with Fourier coefficients $C_1(n),C_2(n)$. For a positive integer $h$ the meromorphic continuation and growth in $s\in\mathbb C$ (away from poles) of the shifted convolution L-function $
Externí odkaz:
http://arxiv.org/abs/2311.06587
Publikováno v:
Sci China Math, 2023, 66
This paper presents a very simple explicit description of Langlands Eisenstein series for ${\rm SL}(n,\mathbb Z)$. The functional equations of these Eisenstein series are heuristically derived from the functional equations of certain divisor sums and
Externí odkaz:
http://arxiv.org/abs/2310.06284
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic number fiel
Externí odkaz:
http://arxiv.org/abs/2304.09071
Fourier coefficients of Eisenstein series figure prominently in the study of automorphic L-functions via the Langlands-Shahidi method, and in various other aspects of the theory of automorphic forms and representations. In this paper, we define Langl
Externí odkaz:
http://arxiv.org/abs/2303.05442
Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on GL(1)) was used by Dirichlet to prove infinitely man
Externí odkaz:
http://arxiv.org/abs/2212.14534
Autor:
Goldfeld, Dorian, Hinkle, Gerhardt
For $d > 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $\mathbb Q\left(\sqrt{-3}\right)$. The Dirichlet series defining $L_d(s)$ converges for $\text{Re}(
Externí odkaz:
http://arxiv.org/abs/2209.11874
This paper introduces the template method for computing the first coefficient of Langlands Eisenstein series on $\GL(n,\mathbb R)$ and more generally on Chevalley groups over the adele ring of $\mathbb Q.$ In brief, the first coefficient of Borel Eis
Externí odkaz:
http://arxiv.org/abs/2007.13268
Autor:
Goldfeld, Dorian, Micheli, Giacomo
In this paper we start by briefly surveying the theory of Fractional Jumps and transitive projective maps. Then, we give an efficient construction of a fractional jump of a projective map and we extend the compound generator construction for the Inve
Externí odkaz:
http://arxiv.org/abs/2001.00474
Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on $\mathrm{GL}(1)$) was used by Dirichlet to prove inf
Externí odkaz:
http://arxiv.org/abs/1910.13586
Autor:
Goldfeld, Dorian, Huang, Bingrong
An automorphic self dual L-function has the super-positivity property if all derivatives of the completed L-function at the central point $s=1/2$ are non-negative and all derivatives at a real point $s > 1/2$ are positive. In this paper we prove that
Externí odkaz:
http://arxiv.org/abs/1803.05394