Hamza Yesilyurt

Affiliation: Bilkent University, Turkey

Email: hamza@fen.bilkent.edu.tr

Title Of Talk: Equalities and inequalities for 7-cores

Abstract: We employ the theory of modular equations to obtain new modular equations of degree seven. Using these identities together with the explicit formulas for the coefficients of 7-cores, we obtain new inequalities involving the coefficients of 7-cores. For example, we show that if n is not 7, than the number of representations of n by the sextenary form x^2+y^2+z^2+7(l^2+t^2+s^2) is larger than the number of 7-cores of n. This is joint work with Alexander Berkovich.

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