Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T09:29:35.886Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  22 January 2016

Shinji Niwa
Shinji Niwa*
Affiliation:
Nagoya University
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.

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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 147 - 161
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

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