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On the infinite products derived from theta series I
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Abstract
Let k be an imaginary quadratic eld, h the complex uperhalf plane, and let τ∈h ∩k,q = eπiτ. In this article, we obtain algebraicnumbers from the 130 identities of Rogers-Ramanujan continued fractionsinvestigated in [28] and [29] by using Berndt’s idea ([3]). Using this, weget special transcendental numbers. For example,q1/ 81 +q1+ q +q21+ q2 + ·([1]) is transcendental.
참고문헌 (10)
- "On a continued fraction of Ramanujan"
- Berndt, "Ramanujan’s remarkable product of theta-functions"
- no, "ON THE INFINITE PRODUCTS DERIVED FROM THETA SERIES I 107"
- Duverney, "Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibona ci numbers"
- A, "The rank and the crank in the theory of partitions", Universityof Susex
- Euler, "Introduction to Analysis of the Innite", Springer-Verlag
- in, "An identity of Ramanujan"
- Ireland, "A Clasical Introduction to Modern Number Theory", Springer-Verlag
- Kim, "Algebraic integer as values of eliptic functions", Acta Arith
- "Tata Lectures on Theta I Modular equations and aproximations to π Second memoir on the xpansion of certain innite products Abel’s theorem on the lemniscate Further identies of the Rogers-Ramanujan type A Course of Modern Analysis", pp.~8, Inc
관련 논문AI추천
Explicit evaluations of Ramanujan's remarkable product of theta-functionM. C. Maheshkumar, M. S. M. Naika장전수학회 · Advanced Studies in Contemporary Mathematics2006 · 제13권 제2호A remark of Eisenstein series and theta series구자경, Daeyeoul Kim대한수학회 · 대한수학회보2002 · 제39권 제2호TWO IDENTITIES INVOLVING THETA FUNCTIONS최준상, Getachew Abiye Salilew, Mahendra Pal Chaudhary영남수학회 · East Asian Mathematical Journal2017 · 제33권 제3호Arithmetic of infinite products and Rogers-Ramanujan continued fractions구자경, 김대열, Yilmaz Simsek대한수학회 · 대한수학회논문집2007 · 제22권 제3호Some Result on Analogous to Ramanujan’s Remarkable Product of Theta FunctionB. N. DHARMENDRA, R. Raghavendra장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호Partial second order mock theta functions, their expansions and Pad\'e approximantsBhaskar Srivastava대한수학회 · 대한수학회지2007 · 제44권 제4호
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