| dc.contributor.advisor |
Đanković, Goran |
|
| dc.contributor.author |
Đokić, Dragan |
|
| dc.date.accessioned |
2023-01-19T13:46:30Z |
|
| dc.date.available |
2023-01-19T13:46:30Z |
|
| dc.date.issued |
2022-11 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/5531 |
|
| dc.description.abstract |
The distribution of primes is determined by the distribution of zeros
of Riemann zeta function, and indirectly by the distribution of magnitude of
this function on the critical line <s =
1
2
. Similarly, in order to consider the
distribution of primes in arithmetic progressions, Dirichlet introduced L-functions
as a generalization of Riemann zeta function. Generalized Riemann hypothesis,
the most important open problem in mathematics, predicts that all nontrivial
zeros of Dirichlet L-function are located on the critical line.
Therefore, one of the main goals in Analytic Number Theory is to consider the
moments of Dirichlet L-functions (according to a certain well defined family). The
relation with the characteristic polynomials of random unitary matrices is one of
the fundamental tools for heuristic understanding of L-functions and derivation
hypotheses about asymptotic formulae for their moments. Asymptotics for even
moments
1
T
Z
T
0
ζ
1
2
+ it
2k
dt,
as T → ∞, is still an open question (except for k = 1, 2), and it is related to the
Lindelöf Hypothesis.
In this dissertation we consider the sixth moment of Dirichlet L-functions
over rational function fields Fq(x), where Fq is a finite field. We will present
the asymptotic formula for the sixth moment with the triple average
X
Q monic
deg Q=d
X
χ (mod Q)
χ odd primitive
2π
Z
log q
0
L
1
2
+ it, χ
6
dt
2π
log q
as d → ∞. All additional averaging is currently necessary to obtain the
asymptotics. The summation over Dirichlet characters and their moduli is
motivated by Bombieri-Vinogradov Theorem. Our result is a function field
analogue of the paper [25] for the corresponding family and averaging over field
Q. Also, our main term confirms the existing Random matrix theory predictions. |
en_US |
| dc.description.provenance |
Submitted by Slavisha Milisavljevic (slavisha) on 2023-01-19T13:46:30Z
No. of bitstreams: 1
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en |
| dc.description.provenance |
Made available in DSpace on 2023-01-19T13:46:30Z (GMT). No. of bitstreams: 1
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Previous issue date: 2022-11 |
en |
| dc.language.iso |
sr |
en_US |
| dc.publisher |
Beograd |
en_US |
| dc.title |
ŠESTI MOMENT DIRIHLEOVIH L-FUNKCIJA NAD RACIONALNIM FUNKCIJSKIM POLJIMA |
en_US |
| mf.author.birth-date |
1992-02-24 |
|
| mf.author.birth-place |
Leskovac |
en_US |
| mf.author.birth-country |
Srbija |
en_US |
| mf.author.residence-state |
Srbija |
en_US |
| mf.author.citizenship |
Srpsko |
en_US |
| mf.author.nationality |
Srbin |
en_US |
| mf.subject.area |
Mathematics |
en_US |
| mf.subject.keywords |
Dirichlet L-functions, moments of L-functions, rational function iii fields, Random matrix theory, Hayes L-functions |
en_US |
| mf.subject.subarea |
Analytic number theory |
en_US |
| mf.contributor.committee |
Lipkovski, Aleksandar |
|
| mf.contributor.committee |
Radovanović, Marko |
|
| mf.contributor.committee |
Stankov, Dragan |
|
| mf.contributor.committee |
Stojadinović, Tanja |
|
| mf.university.faculty |
Mathematical Faculty |
en_US |
| mf.document.references |
84 |
en_US |
| mf.document.pages |
113 |
en_US |
| mf.document.location |
Belgrade |
en_US |
| mf.document.genealogy-project |
No |
en_US |
| mf.university |
Belgrade |
en_US |