Modular forms of half integral weight and the integral of certain theta-functions

Shinji Niwa

doi:10.1017/S0027763000016445

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Recently G. Shimura [1] constructed modular forms of integral weight from the forms of half integral weight. His construction is rather indirect. Indeed, he proved that the Dirichlet series, obtained from a form of half integral weight, multiplied by a certain L-function, corresponds to a modular form of an integral weight by means of the characterization of modular forms due to Weil.

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Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 147 - 161

DOI: https://doi.org/10.1017/S0027763000016445

References

[1] Shimura, G., On modular forms of half integral weight, Ann. of Math., 97 (1973), 440–481.Google Scholar

[2] Shintani, T., On construction of holomorphic cusp forms of half-integral weight, to appear.Google Scholar

[3] Doi, K. and Naganuma, H., On the functional equation of certain Dirichlet series, Inventiones Math., 9 (1969), 1–14.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Vignéras, Marie-France 1977. Modular Functions of One Variable VI. Vol. 627, Issue. , p. 227.

Cohen, Henri 1977. Modular Functions of One Variable VI. Vol. 627, Issue. , p. 175.

Oda, Takayuki 1977. On modular forms associated with indefinite quadratic forms of signature (2,n?2). Mathematische Annalen, Vol. 231, Issue. 2, p. 97.

Rallis, S. and Schiffmann, G. 1977. Automorphic cusp forms constructed from the Weil representation. Bulletin of the American Mathematical Society, Vol. 83, Issue. 2, p. 271.

Kudla, Stephen S. 1977. Modular Functions of One Variable VI. Vol. 627, Issue. , p. 277.

Kudla, Stephen S. 1978. Theta-functions and Hilbert modular forms. Nagoya Mathematical Journal, Vol. 69, Issue. , p. 97.

Asai, Tetsuya 1978. On the Doi-Naganuma lifting associated with imaginary quadratic fields. Nagoya Mathematical Journal, Vol. 71, Issue. , p. 149.

Kudla, Stephen S. 1979. On certain arithmetic automorphic forms forSU (1,q). Inventiones Mathematicae, Vol. 52, Issue. 1, p. 1.

Kojima, Hisashi 1980. Cusp forms of weight 3/2. Nagoya Mathematical Journal, Vol. 79, Issue. , p. 111.

Gelbart, Stephen and Piatetski-Shapiro, I. I. 1980. Distinguished representations and modular forms of half-integral Weight. Inventiones Mathematicae, Vol. 59, Issue. 2, p. 145.

Fomenko, O. M. 1980. Applications of the theory of modular forms to number theory. Journal of Soviet Mathematics, Vol. 14, Issue. 4, p. 1307.

Yoshida, Hiroyuki 1980. Siegel's modular forms and the arithmetic of quadratic forms. Inventiones Mathematicae, Vol. 60, Issue. 3, p. 193.

Kohnen, Winfried 1980. Modular forms of half-integral weight on ?0(4). Mathematische Annalen, Vol. 248, Issue. 3, p. 249.

Gelbart, S. and Piatetski-Shapiro, I. 1981. Automorphic Forms, Representation Theory and Arithmetic. p. 1.

Rallis, S. and Schiffmann, G. 1981. On a relation between ̃𝑆𝐿₂ cusp forms and cusp forms on tube domains associated to orthogonal groups. Transactions of the American Mathematical Society, Vol. 263, Issue. 1, p. 1.

Oda, Takayuki 1981. On the poles of AndrianovL-functions. Mathematische Annalen, Vol. 256, Issue. 3, p. 323.

Ponomarev, Paul 1981. Ternary quadratic forms and Shimura’s correspondence. Nagoya Mathematical Journal, Vol. 81, Issue. , p. 123.

Kohnen, W. and Zagier, D. 1981. Values ofL-series of modular forms at the center of the critical strip. Inventiones Mathematicae, Vol. 64, Issue. 2, p. 175.

Kojima, Hisashi 1981. Siegel modular cusp forms of degree two. Tohoku Mathematical Journal, Vol. 33, Issue. 1,

Maloletkin, G. N. 1982. Construction of Siegel cusp forms of genus two in terms of cusp forms of genus one. Journal of Soviet Mathematics, Vol. 19, Issue. 2, p. 1183.

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