Two new proofs of Lerchβs functional equation
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- by Bruce C. Berndt PDF
- Proc. Amer. Math. Soc. 32 (1972), 403-408 Request permission
Abstract:
One bright Sunday morning I went to church, And there I met a man named Lerch. We both did sing in jubilation, For he did show me a new equation. Two simple derivations of the functional equation of \[ \sum \limits _{n = 0}^\infty {\exp [2\pi inx]{{(n + a)}^{ - s}}} \] are given. The original proof is due to Lerch.References
- M. Lerch, Note sur la fonction ${\mathfrak {K}} \left ( {w,x,s} \right ) = \sum \limits _{k = 0}^\infty {\frac {{e^{2k\pi ix} }}{{\left ( {w + k} \right )^s }}}$, Acta Math. 11 (1887), no.Β 1-4, 19β24 (French). MR 1554747, DOI 10.1007/BF02418041
- E. C. Titchmarsh, Han-shu lun, Science Press, Peking, 1964 (Chinese). Translated from the English by Wu Chin. MR 0197687
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 403-408
- MSC: Primary 10H05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0297721-3
- MathSciNet review: 0297721