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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2019.1
- 수록면
- 377 - 389 (13page)
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We evaluate the convolution sum Wa,b(n) := ∑al+bm=n σ(l)σ(m) for (a, b) = (1, 28), (4, 7), (1, 14), (2, 7) for all positive integers n. We use a modular form approach. We also reevaluate the known sums W1,14(n) and W1,7(n) with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form x21 + x22 + x23 + x24 + 7(x25 + x26 + x27 + x28 ). Finally we express the modular forms 4,7(z), 4,14,1(z) and 4,14,2(z) (given in [10, 14]) as linear combinations of eta quotients
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참고문헌 (18)
참고문헌 신청
S. Alaca / 2014 / Representations by certain octonary quadratic forms whose coefficients are 1, 2, 3 and 6 / Int. J. Number Theory 10:133~150
S. Alaca / 2016 / Evaluation of the convolution sums ∑l+27m=n σ(l)σ(m)and ∑l+32m=n σ(l)σ(m) / Int. J. Number Theory 12:1~13
H. H. Chan / 2008 / Powers of theta functions / Pacific J. Math 235:1~14
S. Cooper / 2009 / Quintic and septic Eisenstein series / Ramanujan J 19:163~181
S. Cooper / 2014 / Evaluation of the convolution sums ∑l+20m=n σ(l)σ(m), ∑4l+5m=n σ(l)σ(m) and ∑2l+5m=n σ(l)σ(m) / Int. J. Number Theory 10:1385~1394
S. Alaca / 2016 / Evaluation of the convolution sums ∑l+27m=n σ(l)σ(m)and ∑l+32m=n σ(l)σ(m) / Int. J. Number Theory 12:1~13
H. H. Chan / 2008 / Powers of theta functions / Pacific J. Math 235:1~14
S. Cooper / 2009 / Quintic and septic Eisenstein series / Ramanujan J 19:163~181
S. Cooper / 2014 / Evaluation of the convolution sums ∑l+20m=n σ(l)σ(m), ∑4l+5m=n σ(l)σ(m) and ∑2l+5m=n σ(l)σ(m) / Int. J. Number Theory 10:1385~1394
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