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DIVISOR FUNCTIONS AND WEIERSTRASS FUNCTIONS ARISING FROM q-SERIES
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 Title & Authors
DIVISOR FUNCTIONS AND WEIERSTRASS FUNCTIONS ARISING FROM q-SERIES
Kim, Dae-Yeoul; Kim, Min-Soo;
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 Abstract
We consider Weierstrass functions and divisor functions arising from -series. Using these we can obtain new identities for divisor functions. Farkas [3] provided a relation between the sums of divisors satisfying congruence conditions and the sums of numbers of divisors satisfying congruence conditions. In the proof he took logarithmic derivative to theta functions and used the heat equation. In this note, however, we obtain a similar result by differentiating further. For any , we have $$k{\cdot}{\tau}_{2;k,l}(n)
 Keywords
divisor function;q-serie;
 Language
English
 Cited by
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ONVOLUTION SUM Σm<n/8σ1(2m)σ1(n-8m),;;;

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CONVOLUTION SUMS ARISING FROM DIVISOR FUNCTIONS,;;;

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3.
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CONVOLUTION SUMS OF ODD AND EVEN DIVISOR FUNCTIONS,;

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ARITHMETIC SUMS SUBJECT TO LINEAR AND CONGRUENT CONDITIONS AND SOME APPLICATIONS,;;;

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1.
CONVOLUTION SUMS OF ODD AND EVEN DIVISOR FUNCTIONS, Honam Mathematical Journal, 2013, 35, 3, 445  crossref(new windwow)
2.
ARITHMETIC SUMS SUBJECT TO LINEAR AND CONGRUENT CONDITIONS AND SOME APPLICATIONS, Honam Mathematical Journal, 2014, 36, 2, 305  crossref(new windwow)
3.
CONVOLUTION SUMS ARISING FROM DIVISOR FUNCTIONS, Journal of the Korean Mathematical Society, 2013, 50, 2, 331  crossref(new windwow)
4.
CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1389  crossref(new windwow)
5.
CONGRUENCES OF THE WEIERSTRASS ${\wp}(x)$ AND ${\wp}^{{\prime}{\prime}}(x)$($x=\frac{1}{2}$, $\frac{\tau}{2}$, $\frac{\tau+1}{2}$)-FUNCTIONS ON DIVISORS, Bulletin of the Korean Mathematical Society, 2013, 50, 1, 241  crossref(new windwow)
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