Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T16:17:59.463Z Has data issue: false hasContentIssue false
  • English
  • Français

Mellin Transforms of Mixed Cusp Forms

Published online by Cambridge University Press:  20 November 2018

Youngju Choie  and
Min Ho Lee
Youngju Choie
Affiliation:
Department of Mathematics Pohang University of Science and Technology Pohang, 790–784 Korea, email: yjc@postech.ac.kr
Min Ho Lee
Affiliation:
Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614 USA, email: lee@math.uni.edu
Rights & Permissions [Opens in a new window]

Abstract

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.

We define generalized Mellin transforms of mixed cusp forms, show their convergence, and prove that the function obtained by such a Mellin transform of a mixed cusp form satisfies a certain functional equation. We also prove that a mixed cusp form can be identified with a holomorphic form of the highest degree on an elliptic variety.

Keywords

11F1211F6611M0614K05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 263 - 273
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Bayer, P. and Neukirch, J., On automorphic forms and Hodge theory. Math. Ann. 257 (1981), 135–155.Google Scholar
[2] Hunt, B. and Meyer, W., Mixed automorphic forms and invariants of elliptic surfaces. Math. Ann. 271 (1985), 53–80.Google Scholar
[3] Kodaira, K., On compact analytic surfaces II. Ann. of Math. 77 (1963), 563–626.Google Scholar
[4] Lang, S., Introduction to modular forms. Springer-Verlag, Heidelberg, 1976.Google Scholar
[5] Laufer, H., On rational singularities. Amer. J. Math. 94 (1972), 597–608.Google Scholar
[6] Lee, M. H., Mixed cusp forms and holomorphic forms on elliptic varieties. Pacific J. Math. 132 (1988), 363–370.Google Scholar
[7] Lee, M. H., Periods of mixed cusp forms. Manuscripta Math. 73 (1991), 163–177.Google Scholar
[8] Lee, M. H., Mixed cusp forms and Poincaré series. Rocky Mountain J. Math. 23 (1993), 1009–1022.Google Scholar
[9] Lee, M. H., Mixed Siegel modular forms and Kuga fiber varieties. Illinois J. Math. 38 (1994), 692–700.Google Scholar
[10] Lee, M. H., Mixed automorphic forms on semisimple Lie groups. Illinois J. Math. 40 (1996), 464–478.Google Scholar
[11] Lee, M. H., Mixed automorphic vector bundles on Shimura varieties. Pacific J. Math. 173 (1996), 105–126.Google Scholar
[12] Miyake, T., Modular forms. Springer-Verlag, Heidelberg, 1989.Google Scholar
[13] Shimura, G., Introduction to the arithmetic theory automorphic functions. Princeton Univ. Press, Princeton, 1971.Google Scholar
[14] Šokurov, V., Holomorphic differential forms of higher degree on Kuga's modular varieties. Math. USSR Sb. 30 (1976), 119–142.Google Scholar
[15] Stiller, P., Special values of Dirichlet series, monodromy, and the periods of automorphic forms. Mem. Amer. Math. Soc. 299, 1984.Google Scholar