Automorphic Forms: Multiplier Systems and Taylor Coefficients
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
Standard
Automorphic Forms : Multiplier Systems and Taylor Coefficients. / von Essen, Flemming Brændgaard.
Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2014. 94 s.Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - BOOK
T1 - Automorphic Forms
T2 - Multiplier Systems and Taylor Coefficients
AU - von Essen, Flemming Brændgaard
PY - 2014
Y1 - 2014
N2 - The Taylor coefficients of weight k Eisenstein series wrt. SL2(Z) are related to values of L-functions for Hecke characters in the point k. We show some congruences for Taylor coefficients of Eisenstein series of weight 4 and 6 and use them to establish congruences for values of L-functions for Hecke characters in the points 4 and 6. It is well known, that all zeros of the Eisenstein series Ek wrt. SL2(Z) in the standard fundamental domain has modulus 1. We show that this is also true for #n Ek, where # is a certain differential operator. We then proceed to study logarithms of multiplier systems. For automorphic forms wrt. Hecke triangle groups and Fuchsian groups with no elliptic elements and genus 0, we show that some logarithms of multiplier systems can be interpreted as a linking number. Finally we show a "twisted" version of the prime geodesics theorem, and logarithms of multiplier systems.
AB - The Taylor coefficients of weight k Eisenstein series wrt. SL2(Z) are related to values of L-functions for Hecke characters in the point k. We show some congruences for Taylor coefficients of Eisenstein series of weight 4 and 6 and use them to establish congruences for values of L-functions for Hecke characters in the points 4 and 6. It is well known, that all zeros of the Eisenstein series Ek wrt. SL2(Z) in the standard fundamental domain has modulus 1. We show that this is also true for #n Ek, where # is a certain differential operator. We then proceed to study logarithms of multiplier systems. For automorphic forms wrt. Hecke triangle groups and Fuchsian groups with no elliptic elements and genus 0, we show that some logarithms of multiplier systems can be interpreted as a linking number. Finally we show a "twisted" version of the prime geodesics theorem, and logarithms of multiplier systems.
UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99122304759905763
M3 - Ph.D. thesis
SN - 978-87-7078-977-6
BT - Automorphic Forms
PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ER -
ID: 123735900