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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.29 No.4
- 발행연도
- 2019.1
- 수록면
- 577 - 590 (14page)
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초록· 키워드
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Let rk(n) denote the number of representations of n as a sum of k squares and tk(n) denote the number of representations of n as a sum of k triangular numbers. Let r , (n) denote the number of representations of n as a sum of times a square and times another square and t , (n) denote the number of representations of n as a sum of times a triangular number and times another triangular number. We prove a number of results in which the generating function of r2(2k(an + b)), r4(2k(an + b)), r1,3(2k(an + b)), t2(2k(an + b)), t1,2(2k(an + b)), for various integer values of k, a and b, is a simple infinite product. We also obtain a relation between t1,3(3k+1n + 3k + 3k−1 · · · +3 + 1) and t1,3(n).
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참고문헌 (8)
참고문헌 신청
C. Adiga / 1985 / Chapter 16 of Ramanujan’s second notebook: Theta functions and q-series / Mem. Amer. Math. Soc. 315:1~91
C. Adiga / 2015 / Hurwitz Type Results for Sum of Two Triangular Numbers / J. Ana. Num. Theor. 3:133~135
P. Barrucand / 2002 / Results of Hurwitz type for five or more squares / Ramanujan J. 6:347~367
B. C. Berndt / 1991 / Ramanujan’s notebooks, Part III / Springer- Verlag
S. Cooper / 2004 / Results of Hurwitz type for three squares / Discrete Math. 274:9~24
C. Adiga / 2015 / Hurwitz Type Results for Sum of Two Triangular Numbers / J. Ana. Num. Theor. 3:133~135
P. Barrucand / 2002 / Results of Hurwitz type for five or more squares / Ramanujan J. 6:347~367
B. C. Berndt / 1991 / Ramanujan’s notebooks, Part III / Springer- Verlag
S. Cooper / 2004 / Results of Hurwitz type for three squares / Discrete Math. 274:9~24
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