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Original Research | Mathematics | Volume 15 Issue 5, May 2026 | Pages: 645 - 646 | India
A Convex Characterization of Bertrand's Postulate via a Legendre-Fenchel Type Transform
Abstract: We establish an equivalence between Bertrand's postulate and a convex-analytic condition involving a Legendre-Fenchel-type transform derived from Euler's totient function. By encoding arithmetic information into a piecewise-affine function and analyzing its dual transform and subdifferential, we obtain a novel interpretation of the existence of primes in the interval (n,2n]. This approach reveals an intrinsic connection between number theory and convex analysis.
Keywords: Bertrand's postulate, Euler's totient function, Legendre-Fenchel transform, subdifferential, convex analysis
How to Cite?: Triloki Nath, "A Convex Characterization of Bertrand's Postulate via a Legendre-Fenchel Type Transform", Volume 15 Issue 5, May 2026, International Journal of Science and Research (IJSR), Pages: 645-646, https://www.ijsr.net/getabstract.php?paperid=SR26508074833, DOI: https://dx.dx.doi.org/10.21275/SR26508074833