Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space. The points could be an infinite collection of electrons ...

In this paper, we derive a class of approximations of the 𝑞-digamma function 𝜓𝑞(𝑥). The infinite family I a ( x;q )=log [ x+a ] q + q x logq 1− q x −( 1 2 −a )H( q−1 )logq, can be used as ...

IF evidence were wanted of the recent progress of the study of pure mathematics on English and American soil, none better could be furnished than the appearance on the two sides of the Atlantic, ...

American Journal of Mathematics, Vol. 138, No. 3 (June 2016), pp. 821-878 (58 pages) Let f be a modular form of weight k and Nebentypus ψ. By generalizing a construction of Dabrowski and Delbourgo, we ...