Relations between theta-functions Hardy sums Eisenstein and Lambert series in the transformation formula of logηg,h(z)
Relations between theta-functions Hardy sums Eisenstein and Lambert series in the transformation formula of logηg,h(z)
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DOI：
10.1016/s0022-314x(02)00072-0
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发表时间：
2003-04
影响因子：
0.7
通讯作者：
Y. Simsek
中科院分区：
文献类型：
--
作者：
Y. Simsek
利用Dedekindeta-函数的广义对数，得到了theta-函数的广义对数。应用这些函数，得到了Hardy和与Theta-函数之间的关系。这些关系的特例给出了Berndt定理6.1-8.1(J.Reine Angew.数学课。303/304(1978)332)和Hardy和的显式公式。利用Dedekin eta函数的对数导数，给出了theta函数的对数与Eisenstein级数之间的关系。利用Lambert级数与广义Dedekin和之间的联系，得到了theta-函数与Lambert级数之间的关系。
In this paper, by using generalized logarithms of Dedekind eta-functions, generalized logarithms of theta-functions are obtained. Applying these functions, the relations between Hardy sums and Theta-functions are found. The special cases of these relations give Berndt's Theorems 6.1–8.1 (J. Reine Angew. Math. 303/304 (1978) 332) and explicit formulae of Hardy sums. Using derivative of logarithms of the Dedekind eta-function, relations between logarithm of the theta-functions and Eisenstein series are given. Applying connection between Lambert series and generalized Dedekind sums, the relation between theta-functions and Lambert series are obtained.