| dc.date.accessioned |
2021-06-08T07:20:14Z |
|
| dc.date.available |
2021-06-08T07:20:14Z |
|
| dc.date.issued |
2021-06-08 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/36096 |
|
| dc.title |
Polynomial and exponential equations modulo primes |
en |
| ethesis.faculty |
Matemaattis-luonnontieteellinen tiedekunta |
fi |
| ethesis.faculty |
Faculty of Science |
en |
| ethesis.faculty |
Matematisk-naturvetenskapliga fakulteten |
sv |
| ethesis.faculty.URI |
http://data.hulib.helsinki.fi/id/8d59209f-6614-4edd-9744-1ebdaf1d13ca |
|
| ethesis.university.URI |
http://data.hulib.helsinki.fi/id/50ae46d8-7ba9-4821-877c-c994c78b0d97 |
|
| ethesis.university |
Helsingin yliopisto |
fi |
| ethesis.university |
University of Helsinki |
en |
| ethesis.university |
Helsingfors universitet |
sv |
| dct.creator |
Järviniemi, Olli |
|
| dct.issued |
2021 |
|
| dct.language.ISO639-2 |
eng |
|
| dct.abstract |
This thesis is motivated by the following questions: What can we say about the set of primes p for which the equation f(x) = 0 (mod p) is solvable when f is (i) a polynomial or (ii) of the form a^x - b?
Part I focuses on polynomial equations modulo primes. Chapter 2 focuses on the simultaneous solvability of such equations. Chapter 3 discusses classical topics in algebraic number theory, including Galois groups, finite fields and the Artin symbol, from this point of view.
Part II focuses on exponential equations modulo primes. Artin's famous primitive root conjecture and Hooley's conditional solution is discussed in Chapter 4. Tools on Kummer-type extensions are given in Chapter 5 and a multivariable generalization of a method of Lenstra is presented in Chapter 6. These are put to use in Chapter 7, where solutions to several applications, including the Schinzel-Wójcik problem on the equality of orders of integers modulo primes, are given. |
en |
| dct.subject |
Prime divisors of polynomials |
|
| dct.subject |
Chebotarev's density theorem |
|
| dct.subject |
Artin's primitive root conjecture |
|
| dct.language |
en |
|
| ethesis.isPublicationLicenseAccepted |
true |
|
| ethesis.language.URI |
http://data.hulib.helsinki.fi/id/languages/eng |
|
| ethesis.language |
englanti |
fi |
| ethesis.language |
English |
en |
| ethesis.language |
engelska |
sv |
| ethesis.thesistype |
pro gradu -tutkielmat |
fi |
| ethesis.thesistype |
master's thesis |
en |
| ethesis.thesistype |
pro gradu-avhandlingar |
sv |
| ethesis.thesistype.URI |
http://data.hulib.helsinki.fi/id/thesistypes/mastersthesis |
|
| dct.identifier.ethesis |
E-thesisID:98248c0d-fc1c-40fa-8302-075121b34e37 |
|
| dct.identifier.urn |
URN:NBN:fi:hulib-202106082543 |
|
| dc.type.dcmitype |
Text |
|
| ethesis.facultystudyline |
Matematiikka |
fi |
| ethesis.facultystudyline |
Mathematics |
en |
| ethesis.facultystudyline |
Matematik |
sv |
| ethesis.facultystudyline.URI |
http://data.hulib.helsinki.fi/id/SH50_050 |
|
| ethesis.mastersdegreeprogram |
Matematiikan ja tilastotieteen maisteriohjelma |
fi |
| ethesis.mastersdegreeprogram |
Master's Programme in Mathematics and Statistics |
en |
| ethesis.mastersdegreeprogram |
Magisterprogrammet i matematik och statistik |
sv |
| ethesis.mastersdegreeprogram.URI |
http://data.hulib.helsinki.fi/id/MH50_001 |
|
