Automorphic Forms: Multiplier Systems and Taylor Coefficients
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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.
Originalsprog | Engelsk |
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Forlag | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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Antal sider | 94 |
ISBN (Trykt) | 978-87-7078-977-6 |
Status | Udgivet - 2014 |
ID: 123735900