The motivic logarithm

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  • Mathematical theories and methods and effective computational algorithms are crucial in coping with the challenges arising in the sciences and in many areas of their application. New concepts and approaches are necessary in order to overcome the complexity barriers particularly created by nonlinearity, high-dimensionality, multiple scales and uncertainty. Combining advanced mathematical and computational methods and computer technology is an essential key to achieving progress, often even in purely theoretical research.

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  • Math is an integral part of our increasingly complex daily life. Calculus for the Managerial, Life, and Social Sciences, Seventh Edition, attempts to illustrate this point with its applied approach to mathematics. Our objective for this Seventh Edition is twofold: (1) to write an applied text that motivates students and (2) to make the book a useful teaching tool for instructors. We hope that with the present edition we have come one step closer to realizing our goal.

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  • We prove that the existence of an automorphism of finite order on a Q-variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Γ-function. This implies that a slight variation of results by Anderson, Colmez and Gross on the periods of CM abelian varieties is valid for a larger class of CM motives. In particular, we prove a weak form of the period conjecture of Gross-Deligne [11, p. 205]1 .

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