SeminarsMultiple zeta values and periods of modular forms
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The multiple zeta values (abbreviated MZVs) are multivariate generalisations of the values of the Riemann zeta function at positive integers. These real number are known to be related with number theory, knot theory, quantum field theory, arithmetic geometry and so on. Our interest in the study of MZVs is a connection with the theory of elliptic modular forms (or their period polynomials), which was first discovered by Don Zagier and then investigated in depth by Gangl, Kaneko and Zagier in the case of depth 2. In my talk, we will provide this connection for arbitrary depths through the study of linear relations among MZVs at the sequences indexed by odd integers greater than 1, modulo lower depth and $¥zeta(2)$. This work is motivated by a certain dimension conjecture proposed by Francis Brown. We finally present an affirmative answer to his dimension conjecture in the case of depth 4.
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Koji Tasaka
2014-11-21
14:00:00 - 15:00:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)
The multiple zeta values (abbreviated MZVs) are multivariate generalisations of the values of the Riemann zeta function at positive integers. These real number are known to be related with number theory, knot theory, quantum field theory, arithmetic geometry and so on. Our interest in the study of MZVs is a connection with the theory of elliptic modular forms (or their period polynomials), which was first discovered by Don Zagier and then investigated in depth by Gangl, Kaneko and Zagier in the case of depth 2. In my talk, we will provide this connection for arbitrary depths through the study of linear relations among MZVs at the sequences indexed by odd integers greater than 1, modulo lower depth and $¥zeta(2)$. This work is motivated by a certain dimension conjecture proposed by Francis Brown. We finally present an affirmative answer to his dimension conjecture in the case of depth 4.
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