We provide a general theorem for evaluating trigonometric Dirichlet series of the form ∑ n>1 f(πnτ) ns , where f is an arbitrary product of the elementary trigonometric functions, τ a real quadratic irrationality and s an integer of the appropriate parity. This unifies a number of evaluations considered by many authors, including Lerch, Ramanujan and Berndt. Our approach is based on relating th...

Please cite this article as: Kamila U. Szulc, Brian W. Timmons, Eric Bouffet, Suzanne Laughlin, Cynthia B. de Medeiros, Jovanka Skocic, Jason P. Lerch, Donald J. Mabbott , Repairing the brain with physical exercise: Cortical thickness and brain volume increases in long-term pediatric brain tumor survivors in response to a structured exercise intervention. The address for the corresponding autho...

We show that the Green’s function of a two dimensional fermion with a modified dispersion relation and short distance parameter a is given by the Lerch zeta function. The Green’s function is defined on a cylinder of radius R and we show that the condition R = a yields the Riemann zeta function as a quantum transition amplitude for the fermion. We formulate the Riemann hypothesis physically as a...

M. K. Tran, J. Levallois, J. Teyssier, A. B. Kuzmenko, G. Autès, O. V. Yazyev, P. Lerch, A. Ubaldini, E. Giannini, D. van der Marel, and A. Akrap Département de la Matière Condensée, University of Geneva, CH-1211 Geneva 4, Switzerland Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland Swiss Light Source, Paul Scherrer Institute, CH-5...

Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of t...

Since our original report (1), we now have 412 patients in the International Hereditary Pancreatitis Registry. Sixteen patients have developed biopsyproven pancreatic cancer, with a parent of origin known for 11 patients—all paternal. Adding the two patients in the recent correspondence by Lerch et al. (2) makes 13 patients with a known parent of origin, of which 11 parents are paternal and two...

With a possible connection to integrals used in General Relativity, we our contour integral method write closed form solution for quadruple involving exponential functions and logarithm of quotient radicals. Almost all Hurwitz–Lerch Zeta have an asymmetrical zero distribution. All the results this work are new.