Advanced search
Publication Cover
Experimental Mathematics Volume 29, 2020 - Issue 3
Submit an article Journal homepage
137
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Imaginary Powers of the Dedekind Eta Function

Bernhard HeimGerman University of Technology in Oman, Muscat, Sultanate of Oman and Max-Planck-Institute for Mathematics, Bonn, GermanyCorrespondence[email protected] [email protected]
,
Markus NeuhauserGerman University of Technology in Oman, Muscat, Sultanate of Oman and RWTH Aachen University, Aachen, Germany
&
Florian RuppCenter of Conflict Resolution & Institute of SocioEconomics, Technische Universität München, Hurwitz Gesellschaft, Bolzmannstr. 3, Garching bei München, Germany
Pages 317-325 | Published online: 04 Jun 2018

References

  • [Aguirre-Hernandez and Loredo-Villalobos 13] B. Aguirre-Hernandez and C. Loredo-Villalobos. Open Problems On Hurwitz Polynomials. Physcon 2013, San Luis Potosi, Mexico, 26–29th August, 2013.
  • [Apostol 76] T. Apostol. Introduction to Analytic Number Theory. New York: Springer, 1976.
  • [Hurwitz 95] A. Hurwitz. “Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt.” Mathematische Annalen 46 (1895), 273–285.
  • [Koecher and Krieg 07] M. Koecher and A. Krieg. Elliptische Funktionen und Modulformen. Berlin: Springer, 2007.
  • [Köhler 11] G. Köhler. Eta Products and Theta Series Identities. Springer Monographs in Mathematics, Berlin: Springer, 2011.
  • [Lehmer 47] D. Lehmer. “The Vanishing of Ramanujan’s τ(n).” Duke Math. J. 14 (1947), 429–433.
  • [Maxwell 68] J. C. Maxwell. “On Governors.” Proceedings of the Royal Society 16 (1868), 270–283.
  • [Newman 55] M. Newman. “An Identity for the Coefficients of Certain Modular Forms.” J. London Math. Soc. 30 (1955), 488–493.
  • [Newman 56] M. Newman. “A Table of the Coefficients of the Powers of η(τ).” Proc. Acad. Amsterdam 59 (1956), 204–216.
  • [Neher 85] E. Neher. “Jacobis Tripleprodukt-Identität und η-Identitäten in der Theorie der affinen Lie-Algebren.” Jahresbericht d. Dt. Math.-Vereinigung 87 (1985), 164–181.
  • [Ono 95] K. Ono. “A Note on the Shimura Correspondence and the Ramanujan τ(n) Function.” Utilitas Math. 47 (1995), 170–180.
  • [Ono and Robins 95] K. Ono and S. Robins. “Superlacunary Cusp Forms.” Proc. AMS 123:N.4 (1995), 1021–1029.
  • [Ono 98] K. Ono. “Gordons ε-Conjecture on the Lacunarity of Modular Forms.” C. R. Math. Rep. Acad. Sci. Canada 20 (1998), 103–107.
  • [Ono 03] K. Ono. “The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series.” Conf. Board Math. Sci. 102 (2003).
  • [Ribet 77] K. Ribet. “Galois Representations Attached to Eigenforms with Nebentypus.” Lect. Notes Math. 601 (1977), 17–52.
  • [Serre 81] J. Serre. “Quelques Applications du Théorèm de Densité de Chebotarov.” Inst. Hautes Études Sci. Pub. Math No. 54 (1981), 323–401.
  • [Serre 85] J. Serre. “Sur la Lacunarité des Puissances de η.” Glasgow Math. J. 27 (1985), 203–221.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.