An elementary proof for the dimension of the graph of the classical Weierstrass function - Keller, Gerhard (Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques, 2015)
Let W_lambda,b(x)=sum_n=0^inftylambda^n g(b^n x) where bgeqslant2 is an integer and g(u)=cos(2pi u) (classical Weierstrass function). Building on work by Ledrappier (1992), Bar'ansky, B'ar'any and Romanowska (2013) and Tsujii (2001), we provide an elementary proof that the Hausdorff dimension of W_lambda,b equals 2+fracloglambdalog b for all lambdain(lambda_b,1) with a suitable lambda_b<1. This reproduces results by Bar'ansky, B'ar'any and Romanowska without using the dimension theory for hyperbolic measures of Ledrappier and Young (1985,1988), which is replaced by a simple telescoping argument together with a recursive multi-scale estimate.