Double zeta values and modular forms

Gangl, H.; Kaneko, M.; Zagier, D.

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. (2006, January). Double zeta values and modular forms. Presented at Automorphic forms and zeta functions, Tokyo, Japan

• Presentation Conference Type: Conference Paper (published)
• Conference Name: Automorphic forms and zeta functions
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1679943
• 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.