The Maximum Number of Zeros of $$r(z) - \overline{z}$$r(z)-z¯ Revisited
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DOI: 10.1007/s40315-017-0231-1
Abstract: Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $$f(z) = \frac{p(z)}{q(z)} - \overline{z}$$f(z)=p(z)q(z)-z¯, which depend on both $$\mathrm{deg}(p)$$deg(p) and $$\mathrm{deg}(q)$$deg(q). Furthermore,… read more here.
Keywords: maximum number; deg; zeros overline; overline revisited ... See more keywords
The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC
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DOI: 10.1007/s40315-020-00305-0
Abstract: Let $$\{\varphi _k\}_{k=0}^\infty $$ { φ k } k = 0 ∞ be a sequence of orthonormal polynomials on the unit circle with respect to a probability measure $$ \mu $$ μ . We study… read more here.
Keywords: variance number; number zeros; theta; theta theta ... See more keywords
On the explicit upper and lower bounds for the number of zeros of the Selberg class
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DOI: 10.1016/j.jnt.2018.07.006
Abstract: In this paper we prove explicit upper and lower bounds for the error term in the Riemann-von Mangoldt type formula for the number of zeros inside the critical strip. Furthermore, we also give examples of… read more here.
Keywords: number zeros; number; upper lower; explicit upper ... See more keywords
Upper bounds for the associated number of zeros of Abelian integrals for two classes of quadratic reversible centers of genus one
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DOI: 10.11948/2018.1959
Abstract: In this paper, by using the method of Picard-Fuchs equation and Riccati equation, we study the upper bounds for the associated number of zeros of Abelian integrals for two classes of quadratic reversible centers of… read more here.
Keywords: zeros abelian; abelian integrals; upper bounds; associated number ... See more keywords