Results 21 to 30 of about 19,492 (245)
One level density of low-lying zeros of families of $L$-functions [PDF]
, 2010 In this paper, we prove some one level density results for low-lying zeros of families of $L$-functions. More specifically, the families under consideration are that of $L$-functions of holomorphic Hecke eigenforms of level 1 and weight $k$ twisted with ...
Davenport +4 more
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A note on Dirichlet characters [PDF]
Mathematics of Computation, 1973 Denoting by r ( k , m , p ) r(k,m,p) the first occurrence of m consecutive kth power residues of a prime p ≡ 1 ( mod k ) p \equiv 1 \pmod k , we show that r ( k ...
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On a Kind of Dirichlet Character Sums [PDF]
Abstract and Applied Analysis, 2013 Letp≥3be a prime and letχdenote the Dirichlet character modulop. For any primeqwithq<p, define the setEq,p=a∣1≤a,a-≤p,aa-≡1modp and a≡a-modq. In this paper, we study a kind of mean value of Dirichlet character sums∑a≤p a∈Eq,pχ(a), and use the properties of the DirichletL-functions and generalized Kloosterman sums to obtain an interesting estimate.
Rong Ma, Yulong Zhang, Guohe Zhang
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Dirichlet characters of the rational polynomials
AIMS Mathematics, 2022 <abstract><p>Denote by $ \chi $ a Dirichlet character modulo $ q\geq 3 $, and $ \overline{a} $ means $ a\cdot\overline{a} \equiv 1 \bmod q $. In this paper, we study Dirichlet characters of the rational polynomials in the form</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \sum\limits ...
Wenjia Guo, Xiaoge Liu, Tianping Zhang
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Dirichlet 𝐿-functions and primitive characters [PDF]
Proceedings of the American Mathematical Society, 1972 It is well known that a Dirichlet L L -function L ( s , χ ) L(s,\chi ) has a functional equation if the character χ \chi is primitive. This note proves the converse result.
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Square-full polynomials in short intervals and in arithmetic progressions [PDF]
, 2016 We study the variance of sums of the indicator function of square-full polynomials in both arithmetic progressions and short intervals. Our work is in the context of the ring $F_{q}[T]$ of polynomials over a finite field $F_{q}$ of $q$ elements, in the ...
Roditty-Gershon, Edva
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Relation of the Cyclotomic Equation with the Harmonic and Derived Series
The Scientific World Journal, 2015 We associate some (old) convergent series related to definite integrals with the cyclotomic equation xm-1=0, for several natural numbers m; for example, for m=3, x3-1=(x-1)(1+x+x2) leads to ∫01dx(1/(1+x+x2))=π/(33)=(1-1/2)+(1/4-1/5)+(1/7-1/8)+⋯.
Luis J. Boya, Cristian Rivera
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The second moment of Dirichlet twists of Hecke $L$-functions [PDF]
, 2009 Fix a Hecke cusp form $f$, and consider the $L$-function of $f$ twisted by a primitive Dirichlet character. As we range over all primitive characters of a large modulus $q$, what is the average behavior of the square of the central value of this $L ...
Gao, Peng +2 more
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Random Characters under the $L$-Measure, I: Dirichlet Characters [PDF]
International Mathematics Research Notices, 2017 We define the $L$-measure on the set of Dirichlet characters as an analogue of the Plancherel measure, once considered as a measure on the irreducible characters of the symmetric group. We compare the two measures and study the limit in distribution of characters evaluations when the size of the underlying group grows.
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Mean values of cubic and quartic Dirichlet characters [PDF]
Functiones et Approximatio Commentarii Mathematici, 2020 12 ...
Gao, Peng, Zhao, Liangyi
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