Abstract
Jacobi’s zeta function has appeared in problems of science and engineering. Thus, its extrema are helpful for solving the related problems. For example, Bowman (Proc Lond Math Soc s2–39:205–215, 1935) used the maximum to calculate the capacity of two-dimensional ordinary condensers when the modulus is very close to one due to practical interest. Since the maximum tends to one in this case, this paper examines the speed of convergence by comparing the maximum minus one with some other functions which converge to zero. Lastly, this paper presents a formula expressed in terms of elementary functions to describe the maximum asymptotically as the reciprocal of the complementary modulus approaches infinity.
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Acknowledgements
I want to thank Prof. Yuan Hu for her detailed explanation on fundamentals of plasma physics that makes Brizard’s article [4] comprehensible to me. Last but not least, I am grateful for the reviewer’s comments used to revise this paper.
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Hu, K. Asymptotic Behavior of the Maximum of Jacobi’s Zeta Function. Results Math 76, 179 (2021). https://doi.org/10.1007/s00025-021-01480-9
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DOI: https://doi.org/10.1007/s00025-021-01480-9