If G is a finite cyclic group
, then #[A.sup.G] = #[A.sub.G] holds.
Among the topics are partition functions and box-spline, the calculus of operator functions, toric Sasaki-Einstein geometry, automorphic representations, rigidity of polyhedral surfaces, number theory techniques in the theory of Lie groups and differential geometry, the flabby glass group of a finite cyclic group
, Green's formula in Hall algebras and cluster algebras, zeta functions in combinatorics and number theory, and soliton hierarchies constructed from involutions.
Let G be a finite cyclic group, and [theta] [member of] G be a generator of G.
The discrete logarithm problem (DPL) in a finite cyclic group G, with a generator [theta] and an element g, is to find the integer a; 0 [less than or equal to] a [less than or equal to] [absolute value of G]-1, such that g = [[theta].sup.a] holds.
Clearly [Z.sub.2][S.sub.n] contains a finite cyclic group
of order [2.sub.n]p.
They illustrate their method with free groups, triangular groups, and finite cyclic groups
, for which they obtain optimal time hypercontractive L2 > Lq inequalities with respect to the Markov process given by the world length and with q an even integer.