Results 211 to 220 of about 10,470,703 (228)

Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers

Research in Number Theory, 2018
New expressions are given for the Fourier expansions of non-holomorphic Eisenstein series with weight k. Among other applications, this leads to non-holomorphic analogs of formulas of Ramanujan, Grosswald and Berndt containing Eichler integrals of ...
C. O’Sullivan
semanticscholar   +1 more source

A criterion of normality based on a single holomorphic function

, 2011
Let F be a family of functions holomorphic on a domain D ⊂ ℂ Let k ≥ 2 be an integer and let h be a holomorphic function on D, all of whose zeros have multiplicity at most k −1, such that h(z) has no common zeros with any f ∈ F.
Xiao Jun Liu, Shahar Nevo
semanticscholar   +1 more source

Holomorphic functions unbounded on curves of finite length

, 2014
Given a pseudoconvex domain , we prove that there is a holomorphic function f on D such that the lengths of paths $$p:\ [0,1] \rightarrow D$$p:[0,1]→D along which $$\mathfrak {R}f$$Rf is bounded above, with p(0) fixed, grow arbitrarily fast as $$p(1 ...
J. Globevnik
semanticscholar   +1 more source

From the holomorphic Wilson loop to ‘d log’ loop-integrands of super-Yang-Mills amplitudes

, 2012
A bstractThe S-matrix for planar $ \mathcal{N} $ = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand
A. Lipstein, L. Mason
semanticscholar   +1 more source

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