The Zeros of Certain Sine-Like Integrals
نویسندگان
چکیده
منابع مشابه
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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Lommel’s function sμ,ν(z) is a particular solution of the differential equation z2y′′ + zy′ + (z2 − ν2)y = zμ+1. Here we present estimates and monotonicity properties of the positive zeros of sμ−1/2,1/2(z) when μ ∈ (0, 1). The positivity of a closely related integral is also considered.
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We locate all of the zeros of certain Poincaré series associated with the Fricke groups Γ0(2) and Γ ∗ 0(3) in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (“On the zeros of Eisenstein series”, 1970).
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We locate all of the zeros of certain Poincaré series associated with the Fricke groups Γ0(2) and Γ ∗ 0(3) in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (“On the zeros of Eisenstein series”, 1970).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1956
ISSN: 0002-9939
DOI: 10.2307/2033543