Skip to main content
minor latex edit and spacing
Source Link
Myshkin
  • 17.6k
  • 5
  • 71
  • 137

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the seminal work of Selberg who developped a a very broad theory which applies to any weakly symmetric Riemannian spaces and not just to symmetric spaces coming from $GL_2$. 

A very good reference that I found on the subject is the book of Tomio Kubota entitled "Elementary theory of Eisenstein series". I found that book extremely well written and very accessible for somebody who wants to learn the subject. I have noticed that this book is not so often cited (as I think it should be) as compared for example to the more recent book of Iwaniec entitled "Spectral methods of Automorphic forms". In fact, I find it very curious that Kubota's book is not even cited once in Iwaniec's book, since after reading the two books, I found a lot of overlaps, especially on the topic surrounding GL_2$GL_2$ real analytic Eisenstein series. 

For a paper that I'm currently writting, I'm planning to cite Kubota's work and give him the proper credits, but before doing so I would like to make sure that I'm not missing an earlier reference on $GL_2$-real analytic Eisenstein series. (besides of course the paramount work of Selberg, Langlands, Harish-Chandra, Gelfand, Pyatetskii-Shapiro who worked in much greater generality).

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the seminal work of Selberg who developped a a very broad theory which applies to any weakly symmetric Riemannian spaces and not just to symmetric spaces coming from $GL_2$. A very good reference that I found on the subject is the book of Tomio Kubota entitled "Elementary theory of Eisenstein series". I found that book extremely well written and very accessible for somebody who wants to learn the subject. I have noticed that this book is not so often cited (as I think it should be) as compared for example to the more recent book of Iwaniec entitled "Spectral methods of Automorphic forms". In fact, I find it very curious that Kubota's book is not even cited once in Iwaniec's book, since after reading the two books, I found a lot of overlaps, especially on the topic surrounding GL_2 real analytic Eisenstein series. For a paper that I'm currently writting, I'm planning to cite Kubota's work and give him the proper credits, but before doing so I would like to make sure that I'm not missing an earlier reference on $GL_2$-real analytic Eisenstein series. (besides of course the paramount work of Selberg, Langlands, Harish-Chandra, Gelfand, Pyatetskii-Shapiro who worked in much greater generality).

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the seminal work of Selberg who developped a a very broad theory which applies to any weakly symmetric Riemannian spaces and not just to symmetric spaces coming from $GL_2$. 

A very good reference that I found on the subject is the book of Tomio Kubota entitled "Elementary theory of Eisenstein series". I found that book extremely well written and very accessible for somebody who wants to learn the subject. I have noticed that this book is not so often cited (as I think it should be) as compared for example to the more recent book of Iwaniec entitled "Spectral methods of Automorphic forms". In fact, I find it very curious that Kubota's book is not even cited once in Iwaniec's book, since after reading the two books, I found a lot of overlaps, especially on the topic surrounding $GL_2$ real analytic Eisenstein series. 

For a paper that I'm currently writting, I'm planning to cite Kubota's work and give him the proper credits, but before doing so I would like to make sure that I'm not missing an earlier reference on $GL_2$-real analytic Eisenstein series (besides of course the paramount work of Selberg, Langlands, Harish-Chandra, Gelfand, Pyatetskii-Shapiro who worked in much greater generality).

edited tags
Link
GH from MO
  • 105.4k
  • 8
  • 293
  • 398
added 2 characters in body
Source Link
Hugo Chapdelaine
  • 7.6k
  • 2
  • 28
  • 70

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the seminal work of Selberg who developped a a very broad theory which applies to any weakly symmetric Riemannian spaces and not just to symmetric spaces coming from $GL_2$. A very good reference that I found on the subject is the book of Tomio Kubota entitled "Elementary theory of Eisenstein series". I found that book extremely well written and very accessible for somebody who wants to learn the subject. I have noticed that this book is not so often cited (as I think it should be) as compared for example to the more recent book of Iwaniec entitled "Spectral methods of Automorphic forms". In fact, I find it very curious that Kubota's book is not even cited once in Iwaniec's book, since after reading the two books, I found a lot of overlaps, especially on the topic surrounding GL_2 real analytic Eisenstein series. For a paper that I'm currently writting, I'm planning to cite Kubota's work and give him the proper credits, but before doing so I would like to make sure that I'm not missing an earlier reference on $GL_2$-real analytic Eisenstein series. (besides of course the paramount work of Selberg, Langlands, Harish-Chandra, Gelfand, Pyatetskii-Shapiro who worked in much greater generality).

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the seminal work of Selberg who developped a a very broad theory which applies to any weakly symmetric Riemannian spaces and not just to symmetric spaces coming from $GL_2$. A very good reference that found on the subject is the book of Tomio Kubota entitled "Elementary theory of Eisenstein series". I found that book extremely well written and very accessible for somebody who wants to learn the subject. I have noticed that this book is not so often cited (as I think it should be) as compared for example to the more recent book of Iwaniec entitled "Spectral methods of Automorphic forms". In fact, I find it very curious that Kubota's book is not even cited once in Iwaniec's book, since after reading the two books, I found a lot of overlaps, especially on the topic surrounding GL_2 real analytic Eisenstein series. For a paper that I'm currently writting, I'm planning to cite Kubota's work and give him the proper credits, but before doing so I would like to make sure that I'm not missing an earlier reference on $GL_2$-real analytic Eisenstein series. (besides of course the paramount work of Selberg, Langlands, Harish-Chandra, Gelfand, Pyatetskii-Shapiro who worked in much greater generality).

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the seminal work of Selberg who developped a a very broad theory which applies to any weakly symmetric Riemannian spaces and not just to symmetric spaces coming from $GL_2$. A very good reference that I found on the subject is the book of Tomio Kubota entitled "Elementary theory of Eisenstein series". I found that book extremely well written and very accessible for somebody who wants to learn the subject. I have noticed that this book is not so often cited (as I think it should be) as compared for example to the more recent book of Iwaniec entitled "Spectral methods of Automorphic forms". In fact, I find it very curious that Kubota's book is not even cited once in Iwaniec's book, since after reading the two books, I found a lot of overlaps, especially on the topic surrounding GL_2 real analytic Eisenstein series. For a paper that I'm currently writting, I'm planning to cite Kubota's work and give him the proper credits, but before doing so I would like to make sure that I'm not missing an earlier reference on $GL_2$-real analytic Eisenstein series. (besides of course the paramount work of Selberg, Langlands, Harish-Chandra, Gelfand, Pyatetskii-Shapiro who worked in much greater generality).

Source Link
Hugo Chapdelaine
  • 7.6k
  • 2
  • 28
  • 70
Loading