Simple exponential estimate for the number of real zeros of complete abelian integrals

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Simple Exponential Estimate for the Number of Real Zeros of Complete Abelian Integrals

One of the main results of this paper is an upper bound for the total number of real isolated zeros of complete Abelian integrals, exponential in the degree of the form (Theorem 1 below). This result improves a previously obtained in [IY1] double exponential estimate for the number of real isolated zeros on a positive distance from the singular locus. In fact, the theorem on zeros of Abelian in...

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linear estimate of the number of zeros of abelian integrals for a kind of quintic hamiltonians

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linear estimate of the number of zeros of abelian integrals for a kind of quintic hamiltonians

we consider the number of zeros of the integral $i(h) = oint_{gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. we prove that the number of zeros of $i(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

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ژورنال

عنوان ژورنال: Annales de l’institut Fourier

سال: 1995

ISSN: 0373-0956

DOI: 10.5802/aif.1478