Theta series and modular forms of level p 2 M

Arnold Pizer

Compositio Mathematica (1980)

  • Volume: 40, Issue: 2, page 177-241
  • ISSN: 0010-437X

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Pizer, Arnold. "Theta series and modular forms of level $p^2M$." Compositio Mathematica 40.2 (1980): 177-241. <http://eudml.org/doc/89433>.

@article{Pizer1980,
author = {Pizer, Arnold},
journal = {Compositio Mathematica},
keywords = {Theta series; modular forms; quaternion algebra; trace formula for Brandt matrices; Hecke operators; canonical involution; W-operators of Atkin- Lehner},
language = {eng},
number = {2},
pages = {177-241},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Theta series and modular forms of level $p^2M$},
url = {http://eudml.org/doc/89433},
volume = {40},
year = {1980},
}

TY - JOUR
AU - Pizer, Arnold
TI - Theta series and modular forms of level $p^2M$
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 40
IS - 2
SP - 177
EP - 241
LA - eng
KW - Theta series; modular forms; quaternion algebra; trace formula for Brandt matrices; Hecke operators; canonical involution; W-operators of Atkin- Lehner
UR - http://eudml.org/doc/89433
ER -

References

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  1. [1] A. Atkin and J. Lehner: Hecke Operators for Γ0(m). Math. Ann.185 (1970) 134-160. Zbl0177.34901
  2. [2] M. Eichler: Zur Zahlentheorie der Quaternionen-Algebren. J. reine angew. Math.195 (1956) 127-151. Zbl0068.03303MR80767
  3. [3] M. Eichler: The Basis problem for modular forms and the traces of the Hecke operators. Lecture Notes in Math. 320, Springer-Verlag, pp. 75-151. Zbl0258.10013MR485698
  4. [4] S. Gelbart: Automorphic Forms on Adele Groups, Annals of Math. Studies No. 83, Princeton Univ. Press (1975). Zbl0329.10018MR379375
  5. [5] H. Hijikata: Explicit formula of the traces of the Hecke operators for Γ0(N): J. Math. Soc. Japan26 (1974) 56-82. Zbl0266.12009
  6. [6] H. Jacquet, R. Langlands: Automorphic Forms on GL(2). Lecture Notes in Math. No. 114, Springer-Verlag (1970). Zbl0236.12010MR401654
  7. [7] J.P. Labesse and R.P. Landlangs: 'L-indistinguishability for SL 2' (preprint)Institute for Advanced Study, Princeton, NJ. 
  8. [8] T. Lam: The Algebraic Theory of Quadratic Forms. W.A. Benjamin, (1973). Zbl0259.10019MR396410
  9. [9] S. Lang: Algebra. Addison-Wesley (1971). Zbl0848.13001MR783636
  10. [9a] W.W. Li: Newforms and Functional Equations. Math. Ann.212 (1975) 285-315. Zbl0278.10026MR369263
  11. [10] A. Ogg: Modular Forms and Dirichlet Series, W.A. Benjamin (1969). Zbl0191.38101MR256993
  12. [11] W. Parry: A negative result on the representation of modular forms by theta series (to appear). Zbl0409.10014MR546669
  13. [12] A. Pizer: On the Arithmetic of Quaternion Algebras II. J. Math. Soc. Japan28 (1976) 676-688. Zbl0344.12005MR432600
  14. [ 13] A. Pizer: The Representability of Modular Forms by Theta Series. J. Math. Soc. Japan28 (1976) 689-698. Zbl0344.10012MR422162
  15. [14] A. Pizer: The Action of the Canonical Involution on Modular Forms of Weight 2 on Γ0(M). Math. Ann.226 (1977) 99-116. Zbl0324.10017
  16. [15] A. Pizer: An Algorithm for Computing Modular Forms on Γ0(N) (to appear). Zbl0433.10012
  17. [16] I. Reiner: Maximal Orders, Academic Press (1975). Zbl0305.16001MR1972204
  18. [17] G. Shimura: Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press (1971). Zbl0221.10029MR314766
  19. [18] C. Siegal: Uber die analytische Theory der quadratic Formen, Gesammelte Abhandlungen, Band I, Springer-Verlag, (1966). 

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