Distribution of Dirichlet l-functions

Stankus, Eugenijus

doi:10.1007/bf00966059

Search citation statements

Order By: Relevance

Paper Sections

Select...

A Laurindikas2

Introduction1

= = 1 + O(1)1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1994

2014

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 6 publications

(4 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that the first theorems of the above type were obtained by P. Elliott [1] and [2], and E. Stankus [5] for Dirichlet L-functions.…”

Section: Introductionmentioning

confidence: 71%

Limit Theorems for Twists of L-Functions of Elliptic Curves. Iv

Garbaliauskienė

Laurinčikas

2014

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

show abstract

“…We note that the first theorems of the above type were obtained by P. Elliott [1] and [2], and E. Stankus [5] for Dirichlet L-functions.…”

Section: Introductionmentioning

confidence: 71%

Limit Theorems for Twists of L-Functions of Elliptic Curves. Iv

Garbaliauskienė

Laurinčikas

2014

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

show abstract

“…A generalization of Theorems 1 and 2 to the complex plane C was given in [4]. Denote by B(S) the class of Borel sets of the space S. Let P be a probability measure on (C, B(C)).…”

Section: A Laurindikasmentioning

confidence: 99%

“…In [4] it was obtained that Wj: Q(~j,kj) = wj(vj,kj) +o (1) for all rj ~ R, hj ~ Z, j = 1 ..... l, as Q --+ oo. So, it remains to consider the functions Wj,h., Q(rj, Th, kj, kh) ..... wOO:, k) of system (2) 9 We will limit ourselves by the study of the function WQ(V, k) only because the asymptotics of the other functions of system (2) can be found in a similar way.…”

Section: A Laurindikasmentioning

confidence: 99%

See 1 more Smart Citation

Multidimensional limit theorem for dirichletL-functions

Laurinčikas¹

1994

Lith Math J

View full text Add to dashboard Cite

Let s = a + it be a complex variable, and let L(s, X) denote the Dirichlet L-function. For L-functions there exist limit theorems which characterize the behavior of L-functions when the modulus of character increases. To state these theorems we need some notation. Let, for Q 7> 2, Z 1 p<~Q X=X (mod p) X~Xo where p denotes a prime number and X0 is the principal character. From the prime number theorem it is easy to deduce that Q2 BQ2Here and further on B denotes a number (not always the same) which is bounded by a constant. We put = F, I2p<~Q X=x(mod p) X 7~Xo .... ,where in place of dots we indicate a condition satisfied by a pair (p,)~ (rood p)). When L (s, X) ~ O, 1/2 < a <~ 1, denote by argL(s, X) the value of the argument of L(s, X) defined by continuous displacement from the point s = 2 along an arc on which l(s, X) does not vanish. Define a distribution function (mod 1) FQ(X) = vQ(argL(s, X)/2rc < x(mod 1)).Then in [1] the following theorem was obtained.THEOREM 1. At each point s in the half-plane a > 1/2 the distribution function (mod 1) FQ(X) converges as Q --+ oo to a continuous distribution function (mod 1) defined by the Fourier transform , ~=, \ m ] p2=~]Here (:t:km/2) denotes the binomial coefficients.

show abstract

Value-distribution of twisted automorphic L-functions

Kolupayeva

Laurinčikas

2008

Lith Math J

View full text Add to dashboard Cite

Distribution of Dirichlet l-functions

Cited by 6 publications

References 3 publications

Limit Theorems for Twists of L-Functions of Elliptic Curves. Iv

Limit Theorems for Twists of L-Functions of Elliptic Curves. Iv

Multidimensional limit theorem for dirichletL-functions

Value-distribution of twisted automorphic L-functions

Contact Info

Product

Resources

About