Abstract
This article is a slightly extended and revised version of a conference talk at “Arithmetik an der A7” in Würzburg, June 23rd, 2017. We present a conjecture on the coincidence of Hecke theta series of weight 1 on three distinct quadratic fields. Then we discuss a special instance of the Deligne–Serre Theorem, implying that the decomposition of prime numbers in a certain extension of the rationals is governed by the coefficients of the eta product \(\eta^{2}(z)\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Deligne, P., Serre, J.-P.: Formes modulaires de poids 1. Ann. Sci. Ec. Norm. Super. 7, 507–530 (1974)
Hecke, E.: Zur Theorie der elliptischen Modulfunktionen. Math. Ann. 97, 210–242 (1926). Math. Werke 23, 428–460
Hiramatsu, T.: Theory of automorphic forms of weight 1. Investig. Number Theory Adv. Stud. Pure Math. 13, 503–584 (1988)
Hiramatsu, T., Saito, S.: An introduction to non-Abelian class field theory. World Scientific, Singapore (2017)
Köhler, G.: Eta products and theta series identities. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg (2011)
Miyake, T.: Modular forms. Springer, Berlin, Heidelberg (1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Köhler, G. Eta products of weight one, and decomposition of primes in non-abelian extensions. Math Semesterber 65, 183–193 (2018). https://doi.org/10.1007/s00591-017-0214-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00591-017-0214-3