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10  Is $\displaystyle \frac{\pi}{e}$ a period? [This was inspired by question Is there a non-trivial definite integral that values to $\frac{e}{\pi}$? ] By a period I mean a number that can be expressed as an integral of an algebraic function over an algebraic domain See What is ... a per...

21  Apologies for the long question. I recall the definition of a (naïve) period according to Kontsevitch and Zagier [KS]: A (naïve) period is a complex number whose real and imaginary parts are absolutely convergent integrals of rational functions with rational coefficients on domains of \$\math... Period (algebraic geometry)
In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, so the periods form a ring. Maxim Kontsevich and Don Zagier gave a survey of periods and introduced some conjectures about them. == Definition == A real number is called a period if it is the difference of volumes of regions of Euclidean space given by polynomial inequalities with rational coefficients. More generally a complex number is called a period if its real and imaginary parts are periods. Periods are numbers that...