Marvin Isadore Knopp

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The aim of this study was to assess stroke rate variability in elite female swimmers (200-m events, all four techniques) by comparing the semi-finalists at the Athens 2004 Olympic Games (n = 64) and semi-finalists at the French National 2004 Championship (n = 64). Since swimming speed (V) is the product of stroke rate (SR) and stroke length (SL), these(More)
We present a new, simple proof, based upon Poisson summation, of the Lipschitz summation formula. A conceptually easy corollary is the functional relation for the Hurwitz zeta function. As a direct consequence we obtain a short, motivated proof of Riemann’s functional equation for ζ(s). Introduction We present a short and motivated proof of Riemann’s(More)
5534 Purpose: Oncogenic defects in the genes involving RAS-RAF-MAPK signaling pathway (RAS, BRAF, or RET/PTC) occur in ∼60% of PTC. VEGF also plays a critical role in thyroid cancer progression. Due to lack of effective treatment, systemic therapy for iodine-refractory PTC is desperately needed. METHODS The primary endpoint of this phase II trial was to(More)
L It is a result familiar in the theory of automorphic form s that an entire automorphic form of positive dimension on an H-group is identically zero (see sec. 2 for the definitions). This follows immediately , for exa mple, from the well-known exac t formula for the Fourier coefficie nts of automorphic forms of positive dimension ([1], p. 314).1 Another(More)
In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier [37] which played an important role in the construction by Kohnen and Zagier [26] of a kernel function for the Shimura and Shintani lifts between half-integral and integral weight cusp(More)
We survey the theory of vector-valued modular forms and their connections with modular differential equations and Fuchsian equations over the threepunctured sphere. We present a number of numerical examples showing how the theory in dimensions 2 and 3 leads naturally to close connections between modular forms and hypergeometric series.
The numerator over c is the Ramanujan sum ∑ (a,c)=1 cos( 2πma c ). This identity clearly displays the oscillations of σ(m) around its mean value π m 6 . Also, (1.1) makes sense as a limit when m = 0 and gives the extension σ(0) = − 1 24 . There is a nice generalization of Ramanujan’s formula, that goes back to Petersson and Rademacher, that connects it with(More)