Double zeta values and modular forms

Gangl, H.; Kaneko, M.; Zagier, D.; Böecherer, S.; Ibukiyama, T.; Sato, F.

Abstract

We give new relations among double zeta values and show that the structure of the Q-vector space of all (known) relations among double zeta values of weight k is connected in many different ways with the structure of the space of modular forms of weight k on the full modular group. Furthermore, we introduce and study both transcendental and combinatorial ``double Eisenstein series'' which explain the relation between double zeta values and modular forms and provide new realizations of the space of double zeta relations.

Citation

Gangl, H., Kaneko, M., Zagier, D., Böecherer, S., Ibukiyama, T., & Sato, F. (2006). Double zeta values and modular forms. In Automorphic forms and zeta functions : proceedings of the conference in memory of Tsuneo Arakawa, 4-7 September 2004, Rikkyo University, Japan (71-106)

• Conference Name: Automorphic forms and zeta functions
• Conference Location: Tokyo, Japan
• Publication Date: Jan 1, 2006
• Deposit Date: Jul 26, 2007
• Publisher: World Scientific Publishing
• Pages: 71-106
• Book Title: Automorphic forms and zeta functions : proceedings of the conference in memory of Tsuneo Arakawa, 4-7 September 2004, Rikkyo University, Japan.
• Keywords: Multiple zeta values, Modular forms, Period polynomials, Double Eisenstein series.
• Publisher URL: http://www.worldscibooks.com/mathematics/6005.html
• Additional Information: Proceedings of the Conference in Memory of Tsuneo Arakawa, Rikkyo University, Japan 4 - 7 September 2004.