Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-05T06:06:56.434Z Has data issue: false hasContentIssue false

On the Niwa-Shintani theta-kernel lifting of modular forms

Published online by Cambridge University Press:  22 January 2016

Barry A. Cipra*
Affiliation:
Department of Mathematics, Ohio State University Columbus, Ohio U8210USA
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Modular forms of half-integral weight are of intrinsic interest: many of the functions of classical number theory transform under a matrix group with half-integral weight. The aim of this paper is to refine some results and techniques which have been introduced to study these functions and the arithmetic information which they contain.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[1] Cohen, H. and Oesterlé, J., Dimensions des espaces de formes modulaires, Modular Functions of One Variable VI, Lecture Notes in Math., Springer-Verlag, 627(1977), 69-78.Google Scholar
[2] Flicker, Y., Automorphic forms on covering groups of GL(2), Invent. Math., 57(1980), 119182.Google Scholar
[3] Gelbart, S. and Piatetski-Shapiro, I., On Shimura’s Correspondence for Modular Forms of Half-Integral Weight, Proc, Colloquium on Automorphic Forms, Representation Theory and Arithmetic, Bombay, 1979.Google Scholar
[4] Hecke, E., Analytische Arithmetik der Positiven Quadratischen Formen, Kgl. Danske Videnskabernes Selskab. Mathematisk-Fysiske Meddelelser, XVII, 12 (1940), 1348, (═Werke, 789918).Google Scholar
[5] Hecke, E., Théorie der Eisensteinschen Reinen Höherer Stufe und Ihre Anwendung auf Funktiontheorie und Arithmetik, Abhand. Math. Seminar Hamburg, 5 (1927), 199224, (═Werke, 461486).Google Scholar
[6] Igusa, J., Theta Functions, Springer-Verlag, 1972.Google Scholar
[7] Kojima, H., Cusp forms of weight 3/2, Nagoya Math. J., 79(1980), 111122.Google Scholar
[8] Niwa, S., Modular forms of half integral weight and the integral of certain thetafunctions, Nagoya Math. J., 56 (1974), 147161.Google Scholar
[9] Petersson, H., Über die Berechnung der Skalarprodukte ganzer Modulformen, Comment. Math. Helv., 22(1949), 168199.Google Scholar
[10] Serre, J.-P. and Stark, H., Modular forms of weight 1/2, Modular Functions of One Variable VI, Lecture Notes in Math., Springer-Verlag, 627 (1977), 2967.Google Scholar
[11] Shimura, G., On modular forms of half integral weight, Ann. of Math., 97 (1973), 440481.Google Scholar
[12] Shintani, T., On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83126.CrossRefGoogle Scholar
[13] Cohen, H., A lifting of modular forms in one variable to Hilbert modular forms in two variables, Modular Functions of One Variable VI, Lecture Notes in Math., Springer-Verlag, 627(1977), 175196.Google Scholar