Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2

A. Biró

Acta Arithmetica (2000)

  • Volume: 94, Issue: 2, page 103-152
  • ISSN: 0065-1036

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Biró, A.. "Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2." Acta Arithmetica 94.2 (2000): 103-152. <http://eudml.org/doc/207427>.

@article{Biró2000,
author = {Biró, A.},
journal = {Acta Arithmetica},
keywords = {Maass form; congruence subgroup; -function; Shimura lift},
language = {eng},
number = {2},
pages = {103-152},
title = {Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2},
url = {http://eudml.org/doc/207427},
volume = {94},
year = {2000},
}

TY - JOUR
AU - Biró, A.
TI - Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 2
SP - 103
EP - 152
LA - eng
KW - Maass form; congruence subgroup; -function; Shimura lift
UR - http://eudml.org/doc/207427
ER -

References

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  4. [Du] Duke, W., Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), 73-90. Zbl0628.10029
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  9. [Ko1] Kohnen, W., Modular forms of half-integral weight on Γ 0 ( 4 ) , Math. Ann. 248 (1985), 249-266. 
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  13. [K] Kuznetsov, N. V., Petersson's conjecture for cusp forms of weight 0 and Linnik's conjecture. Sums of Kloosterman sums, Mat. Sb. 111 (1980), 334-383 (in Russian). Zbl0427.10016
  14. [La] Landau, E., Vorlesungen über Zahlentheorie, 3 vol., Hirzel, Leipzig, 1927. 
  15. [Le] Lebedev, N. N., Special Functions and their Applications, 2nd ed., Moscow, 1963. 
  16. [M] Maass, H., Über die räumliche Verteilung der Punkte in Gittern mit indefiniter Metrik, Math. Ann. 138 (1959), 287-315. Zbl0089.06102
  17. [M-O] Magnus, O., and Oberbettinger, F., Formulas and Theorems for the Functions of Mathematical Physics, Springer, Berlin, 1966. 
  18. [N] Niwa, S., Modular forms of half-integral weight and the integral of certain theta functions, Nagoya Math. J. 56 (1974), 147-161. 
  19. [P] Proskurin, N. V., General Kloosterman sums, preprint LOMI R-3-80, Akad. Nauk SSSR Mat. Inst. Leningr. Otd. (1980) (in Russian), MR 82E 10040. 
  20. [P-Sz] Pólya, G., and Szegö, G., Problems and Theorems in Analysis, Vol. 1, Springer, Berlin, 1972. 
  21. [Shim] Shimura, G., On modular forms of half-integral weight, Ann. of Math. (2) 97 (1973), 440-481. Zbl0266.10022
  22. [Shin] Shintani, T., On construction of holomorphic cusp forms of half-integral weight, Nagoya Math. J. 58 (1975), 83-126. Zbl0316.10016
  23. [Wal] Waldspurger, J. L., Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375-484. Zbl0431.10015
  24. [W] Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, 1952. 

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