Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Superlacunary cusp forms


Authors: Ken Ono and Sinai Robins
Journal: Proc. Amer. Math. Soc. 123 (1995), 1021-1029
MSC: Primary 11F37; Secondary 11F11, 11F32
MathSciNet review: 1242101
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Many researchers have studied Euler product identities of weight $ k = \frac{1}{2}$ and $ k = \frac{3}{2}$, often related to the Jacobi Triple Product identity and the Quintuple Product identity. These identities correspond to theta series of weight $ k = \frac{1}{2}$ and $ k = \frac{3}{2}$, and they exhibit a behavior which is defined as superlacunary. We show there are no eigen-cusp forms of integral weight which are superlacunary. For half-integral weight forms with $ k \geq \frac{5}{2}$, we give a mild condition under which there are no superlacunary eigen-cusp forms. These results suggest the nonexistence of similar Euler-Product identities that arise from eigen-cusp forms with weight $ k \ne \frac{1}{2}$ or $ \frac{3}{2}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11F37, 11F11, 11F32

Retrieve articles in all journals with MSC: 11F37, 11F11, 11F32


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1242101-2
PII: S 0002-9939(1995)1242101-2
Keywords: Modular forms, lacunarity, superlacunarity
Article copyright: © Copyright 1995 American Mathematical Society