Cancellation in algebraic twisted sums on GL_ m

2021 ◽  
Vol 33 (4) ◽  
pp. 1061-1082
Author(s):  
Yujiao Jiang ◽  
Guangshi Lü
Keyword(s):  
Dirichlet Series ◽  
Central Character ◽  
Multiplicative Functions ◽  
Cuspidal Representation ◽  
Series Coefficient

Abstract Let π be an automorphic irreducible cuspidal representation of GL m {\operatorname{GL}_{m}} over ℚ {\mathbb{Q}} with unitary central character, and let λ π ⁢ ( n ) {\lambda_{\pi}(n)} be its n-th Dirichlet series coefficient. We study short sums of isotypic trace functions associated to some sheaves modulo primes q of bounded conductor, twisted by multiplicative functions λ π ⁢ ( n ) {\lambda_{\pi}(n)} and μ ⁢ ( n ) ⁢ λ π ⁢ ( n ) {\mu(n)\lambda_{\pi}(n)} . We are able to establish non-trivial bounds for these algebraic twisted sums with intervals of length of at least q 1 / 2 + ε {q^{1/2+\varepsilon}} for an arbitrary fixed ε > 0 {\varepsilon>0} .

The Calculation and Estimate of Interval-Valued and Fuzzy Dirichlet Series Coefficient

2013 ◽  
Vol 325-326 ◽  
pp. 1515-1518
Author(s):  
Yu Duan ◽  
Hong Jian Luo
Keyword(s):  
Dirichlet Series ◽  
Series Coefficient ◽  
Definition Of ◽  
Interval Valued

This article gives the definition of interval-valued Dirichlet series. Based on [1, , this article discusses some properties about the coefficient of interval-valued and fuzzy Dirichlet series. Ihe calculation of coefficient , of interval-valued Dirichlet series and the coefficient of fuzzy Dirichelt series are also discussed. Moreover, some relative theorems and properties are presented.

scholarly journals Two Linnik-type problems for automorphic L-functions

2011 ◽  
Vol 151 (2) ◽  
pp. 219-227 ◽  
Author(s):  
JIANYA LIU ◽  
YAN QU ◽  
JIE WU
Keyword(s):  
Dirichlet Series ◽  
Half Plane ◽  
Implied Constant ◽  
Cuspidal Representation ◽  
Sign Change ◽  
Series Expression

AbstractLet m ≥ 2 be an integer, and π an irreducible unitary cuspidal representation for GLm(), whose attached automorphic L-function is denoted by L(s, π). Let {λπ(n)}n=1∞ be the sequence of coefficients in the Dirichlet series expression of L(s, π) in the half-plane ℜs > 1. It is proved in this paper that, if π is such that the sequence {λπ(n)}n=1∞ is real, then the first sign change in the sequence {λπ(n)}n=1∞ occurs at some n ≪ Qπ1 + ϵ, where Qπ is the conductor of π, and the implied constant depends only on m and ϵ. This improves the previous bound with the above exponent 1 + ϵ replaced by m/2 + ϵ. A result of the same quality is also established for {Λ(n)aπ(n)}n=1∞, the sequence of coefficients in the Dirichlet series expression of −(L′/L)(s, π) in the half-plane ℜs > 1.

HYPERTRANSCENDENCE OF -FUNCTIONS FOR

2015 ◽  
Vol 93 (3) ◽  
pp. 388-399
Author(s):  
HIROFUMI NAGOSHI
Keyword(s):  
Zeta Function ◽  
Dirichlet Series ◽  
Riemann Zeta Function ◽  
Automorphic Representation ◽  
Functional Difference ◽  
Central Character ◽  
Cuspidal Automorphic Representation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Algebraic Difference

We generalise a result of Hilbert which asserts that the Riemann zeta-function${\it\zeta}(s)$is hypertranscendental over$\mathbb{C}(s)$. Let${\it\pi}$be any irreducible cuspidal automorphic representation of$\text{GL}_{m}(\mathbb{A}_{\mathbb{Q}})$with unitary central character. We establish a certain type of functional difference–differential independence for the associated$L$-function$L(s,{\it\pi})$. This result implies algebraic difference–differential independence of$L(s,{\it\pi})$over$\mathbb{C}(s)$(and more strongly, over a certain field${\mathcal{F}}_{s}$which contains$\mathbb{C}(s)$). In particular,$L(s,{\it\pi})$is hypertranscendental over$\mathbb{C}(s)$. We also extend a result of Ostrowski on the hypertranscendence of ordinary Dirichlet series.

scholarly journals Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots

2014 ◽  
Vol Volume 37 ◽  
Author(s):  
Sankar Sitaraman
Keyword(s):  
Dirichlet Series ◽  
Mean Value ◽  
Multiplicative Functions ◽  
New Approach ◽  
Mean Values ◽  
Artin's Conjecture ◽  
International Audience ◽  
The Mean ◽  
Primitive Roots

International audience We discuss how one could study asymptotics of cyclotomic quantities via the mean values of certain multiplicative functions and their Dirichlet series using a theorem of Delange. We show how this could provide a new approach to Artin's conjecture on primitive roots. We focus on whether a fixed prime has a certain order modulo infinitely many other primes. We also give an estimate for the mean value of one such Dirichlet series.

Criss-Cross: Identity and Transformation in Re-reading Billy Elliot

2016 ◽  
Vol 13 (4) ◽  
pp. 536-551
Author(s):  
Jacqui Miller
Keyword(s):  
Identity Formation ◽  
Gender And Sexuality ◽  
Central Character ◽  
Theoretical Frameworks ◽  
Liberal Politics ◽  
Starting Point ◽  
And Gender ◽  
Opening Up

Billy Elliot (2000) has been widely recognised as an important British film of the post-Thatcher period. It has been analysed using multiple disciplinary methodologies, but almost always from the theoretical frameworks of class and gender/sexuality. The film has sometimes been used not so much as a focus of analysis itself but as a conduit for exploring issues such as class deprivation or neo-liberal politics and economics. Such studies tend to use the film's perceived shortcomings as a starting point to critique society's wider failings to interrogate constructions of gender and sexuality. This article argues that an examination of the identity formation of some of the film's subsidiary characters shows how fluidity and transformation are key to the film's opening up of a jouissance which is enabled by but goes beyond its central character.

ANALISIS STRUKTUR SOSIAL CERITA DALAM CERITA PENDEK ANAK “ANGGREK RARA” (SEBUAH KAJIAN SOSIOLOGI SASTRA TERHADAP SASTRA ANAK)

2017 ◽  
Vol 3 (2) ◽  
pp. 184
Author(s):  
Sari Herleni
Keyword(s):  
Social Structure ◽  
Short Story ◽  
Real Life ◽  
Central Character ◽  
The Real ◽  
Social Fact ◽  
The Social ◽  
Family Home

This article describes about the figure of children world in a short story “Anggrek Rara” written by Ina Inong, by connecting the social structure in the text and in the real life. After analyzing the social structure in the story, it is found that the plot of this story was the progressive plot, the background was from the social fact that came from inner house and outer house, otherwise the central character were Rara and Bunda. By analyzing social structure of text, it was found that a family (home) is the serious and formal environment while outer house is free and non formal. The result of the research showed that the children short story “ Anggrek Rara” was expected to give the figure outlines of the children world.AbstrakPenelitian ini membahas tentang gambaran dunia anak dalam cerita pendek anak “Anggrek Rara” karya Ina Inong dengan menghubungkan struktur sosial teks dalam karya dan struktur sosial teks dengan realitas. Melalui analisis struktur sosial dalam karya terungkap bahwa alur cerita ini merupakan alur lurus, latar terdiri dari fakta sosial yang bersumber dari rumah dan di luar rumah, sedangkan tokoh Rara dan Bunda adalah tokoh sentral. Melalui analisis struktur sosial teks dengan realitas terungkap bahwa keluarga (rumah) merupakan lingkungan yang sifatnya serius dan formal, sedangkan di luar rumah bahkan bersifat bebas dan non formal. Hasil yang diperoleh dari analisis ini menunjukkan bahwa cerita pendek anak “Anggrek Rara” dianggap mampu memberikan garis-garis besar gambaran kehidupan dunia anak.

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