FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W202009209> ?p ?o ?g. }

• W202009209 abstract "In this thesis, we present four problems related to elliptic curves, modular forms, the distribution of primes, or some combination of the three. The first chapter surveys the relevant background material necessary for understanding the remainder of the thesis. The four following chapters present our problems of interest and their solutions. In the final chapter, we present our conclusions as well as a few possible directions for future research. Hurwitz class numbers are known to have connections to many areas of number theory. In particular, they are intimately connected to the theory of binary quadratic forms, the structure of imaginary quadratic number fields, the theory of elliptic curves, and the theory of modular forms. Hurwitz class number identities of a certain type are studied in Chapter 2. To prove these identities, we demonstrate three different techniques. The first method involves a relation between the Hurwitz class number and elliptic curves, while the second and third methods involve connections to modular forms. In Chapter 3, we explore the construction of finite field elements of high multiplicative order arising from modular curves. The field elements are constructed recursively using the equations that Elkies discovered to describe explicit modular towers. Using elementary techniques, we prove lower bounds for the orders of these elements. Prime distribution has been a central theme in number theory for hundreds of years. Mean square error estimates for the Chebotarev Density Theorem are proved in Chapter 4. These estimates are related to the classical Barban-Davenport-Halberstam Theorem and will prove to be indispensable for our work in Chapter 5, where we take up the study of the Lang-Trotter Conjecture “on average” for elliptic curves defined over number fields." @default.
• W202009209 created "2016-06-24" @default.
• W202009209 creator A5032466562 @default.
• W202009209 date "2009-01-01" @default.
• W202009209 modified "2023-09-27" @default.
• W202009209 title "On Elliptic Curves, Modular Forms, and the Distribution of Primes" @default.
• W202009209 cites W1496801598 @default.
• W202009209 cites W1498769399 @default.
• W202009209 cites W1515360960 @default.
• W202009209 cites W1528542528 @default.
• W202009209 cites W1868013030 @default.
• W202009209 cites W1888723546 @default.
• W202009209 cites W1964637560 @default.
• W202009209 cites W1976677460 @default.
• W202009209 cites W1987494994 @default.
• W202009209 cites W1988456412 @default.
• W202009209 cites W1993515438 @default.
• W202009209 cites W2001572759 @default.
• W202009209 cites W2004055500 @default.
• W202009209 cites W2005376004 @default.
• W202009209 cites W2008808943 @default.
• W202009209 cites W2026614052 @default.
• W202009209 cites W2038741633 @default.
• W202009209 cites W2041872495 @default.
• W202009209 cites W2049076424 @default.
• W202009209 cites W2050533226 @default.
• W202009209 cites W2050970960 @default.
• W202009209 cites W2060437372 @default.
• W202009209 cites W2062780395 @default.
• W202009209 cites W2148965379 @default.
• W202009209 cites W2271040601 @default.
• W202009209 cites W2322172566 @default.
• W202009209 cites W2330548796 @default.
• W202009209 cites W2333976070 @default.
• W202009209 cites W2554625905 @default.
• W202009209 cites W40577338 @default.
• W202009209 cites W130201419 @default.
• W202009209 cites W3203668817 @default.
• W202009209 hasPublicationYear "2009" @default.
• W202009209 type Work @default.
• W202009209 sameAs 202009209 @default.
• W202009209 citedByCount "0" @default.
• W202009209 crossrefType "journal-article" @default.
• W202009209 hasAuthorship W202009209A5032466562 @default.
• W202009209 hasConcept C110121322 @default.
• W202009209 hasConcept C113429393 @default.
• W202009209 hasConcept C114614502 @default.
• W202009209 hasConcept C118615104 @default.
• W202009209 hasConcept C121444067 @default.
• W202009209 hasConcept C129844170 @default.
• W202009209 hasConcept C134306372 @default.
• W202009209 hasConcept C154945302 @default.
• W202009209 hasConcept C166437778 @default.
• W202009209 hasConcept C169654258 @default.
• W202009209 hasConcept C179603306 @default.
• W202009209 hasConcept C184992742 @default.
• W202009209 hasConcept C195831351 @default.
• W202009209 hasConcept C197875053 @default.
• W202009209 hasConcept C202444582 @default.
• W202009209 hasConcept C2524010 @default.
• W202009209 hasConcept C2777212361 @default.
• W202009209 hasConcept C33923547 @default.
• W202009209 hasConcept C40758505 @default.
• W202009209 hasConcept C41008148 @default.
• W202009209 hasConcept C42747912 @default.
• W202009209 hasConcept C59766168 @default.
• W202009209 hasConcept C73683783 @default.
• W202009209 hasConcept C75764964 @default.
• W202009209 hasConcept C77926391 @default.
• W202009209 hasConcept C80695182 @default.
• W202009209 hasConcept C95136341 @default.
• W202009209 hasConcept C9652623 @default.
• W202009209 hasConceptScore W202009209C110121322 @default.
• W202009209 hasConceptScore W202009209C113429393 @default.
• W202009209 hasConceptScore W202009209C114614502 @default.
• W202009209 hasConceptScore W202009209C118615104 @default.
• W202009209 hasConceptScore W202009209C121444067 @default.
• W202009209 hasConceptScore W202009209C129844170 @default.
• W202009209 hasConceptScore W202009209C134306372 @default.
• W202009209 hasConceptScore W202009209C154945302 @default.
• W202009209 hasConceptScore W202009209C166437778 @default.
• W202009209 hasConceptScore W202009209C169654258 @default.
• W202009209 hasConceptScore W202009209C179603306 @default.
• W202009209 hasConceptScore W202009209C184992742 @default.
• W202009209 hasConceptScore W202009209C195831351 @default.
• W202009209 hasConceptScore W202009209C197875053 @default.
• W202009209 hasConceptScore W202009209C202444582 @default.
• W202009209 hasConceptScore W202009209C2524010 @default.
• W202009209 hasConceptScore W202009209C2777212361 @default.
• W202009209 hasConceptScore W202009209C33923547 @default.
• W202009209 hasConceptScore W202009209C40758505 @default.
• W202009209 hasConceptScore W202009209C41008148 @default.
• W202009209 hasConceptScore W202009209C42747912 @default.
• W202009209 hasConceptScore W202009209C59766168 @default.
• W202009209 hasConceptScore W202009209C73683783 @default.
• W202009209 hasConceptScore W202009209C75764964 @default.
• W202009209 hasConceptScore W202009209C77926391 @default.
• W202009209 hasConceptScore W202009209C80695182 @default.
• W202009209 hasConceptScore W202009209C95136341 @default.
• W202009209 hasConceptScore W202009209C9652623 @default.

• next