In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic ...

In this paper we shall prove that the combination of the general distribution property and the functional equation for the Lipschitz-Lerch transcendent capture the whole spectrum of deeper results on the relations between the values at rational arguments of functions of a class of zeta-functions. By Theorem 1 and its corollaries, we can cover all the previous results in a rather simple and luci...

References: [1] E.J. Slow, et al, “Selective striatal neuronal loss in a YAC128 mouse model of Huntington disease.,” Hum Mol Genet, vol. 12, 2003, p. 1555―67. [2] J.M. Van Raamsdonk, et al, “Selective degeneration and nuclear localization of mutant huntingtin in the YAC128 mouse model of Huntington disease.,” Hum Mol Genet, vol. 14, 2005, p. 3823―35. [3] J.P. Lerch, et al, “Automated deformatio...

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada Department of Applied Mathematics, Donghua University, Shanghai, People’s Republic of China Department of Mathematics, M. P. University of Agriculture and Technology, Rajasthan, India *Corresponding author: [email protected] Received September 15, 2013; Revised October 22, 2013; Accepted Nov...

Association between CVR impairment and cortical thinning in children with sickle cell disease Junseok Kim, Jackie Leung, Jason Lerch, Suzan Williams, and Andrea Kassner Medical Imaging, University of Toronto, Toronto, Ontario, Canada, Physiology and Experimental Medicine, The Hospital for Sick Children, Toronto, Ontario, Canada, MICe, Toronto Center for Phenogenomics, Toronto, Ontario, Canada, ...

The analytic properties of the standard twist $F(s,\alpha)$, where $F(s)$ belongs to a wide class $L$-functions, are prime importance in describing structure Selberg class. In this paper we present deeper study such properties. particular, show that $F(s,\alpha)$ satisfies functional equation new type, somewhat resembling Hurwitz-Lerch zeta function. Moreover, detect finer polar characterizing ...

Abstract According to the theory of regular geometric functions, relevance geometry analysis is a critical feature. One significant tools study operators utilize convolution product. The dynamic techniques have attracted numerous complex analyses in current research. In this effort, an attempt made by utilizing said new linear operator connecting incomplete beta function and Hurwitz–Lerch zeta ...

This manuscript concerns two definite integrals that could be connected to the Bose-Einstein and Fermi-Dirac functions in integrands, separately, with numerators slightly modified a difference expressions contain Fourier kernel multiplied by polynomial its complex conjugate. In this work, we use our contour integral method derive these integrals, which are given ∫0∞ie−imx(log(a)−ix)k−eimx(log(a...