Speaker: Emanuel Guariglia, São Paulo State University, Brazil; Kean University, USA; Fenerbahçe University, Turkey.

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

MS Teams : A MS Teams link will appear here, an hour before the talk. For best experince, please download the app.

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: fractional derivative, zeta functions, functional equation, prime numbers, Shannon entropy

Abstract: In this talk, we provide an overview on the role of zeta functions in fractional calculus. More precisely, we deal with the functional equations for the fractional derivative of zeta functions. Moreover, we discuss the link between these fractional derivatives and the distribution of prime numbers. Finally, we give two applications in Shannon entropy and signal theory.

Biography: Emanuel Guariglia was born in Agropoli, Southern Italy. He received his education at University of Naples Federico II, Naples and University of Salerno, Fisciano, graduating in Telecommunications Engineering (Bachelor and Master) and Mathematics (PhD).

He was Postdoctoral Researcher at São Paulo State University, Brazil (2020-2022). Apart from fractional calculus, his research interests include fractal geometry, applied functional analysis, wavelet analysis, analytic number theory and dynamical systems.

He was visiting PhD student at Mälardalen University (Sweden) for 18 months. During this time, he won the Best Student Award at the ICNPAA 2016 World Congress (La Rochelle, France, 4-8 July 2016) for the scientific paper titled “A functional derivative for the Riemann zeta fractional derivative”. Last month he received another award for his scientific contribution at the 14th International Conference on Artificial Intelligence and Applied Mathematics (Al-Hoceima, Morocco, 12-13 May 2026). Emanuel Guariglia is in the World’s Top 2\% Scientists most-cited scientists by Stanford University

Bibliography

[1] Apostol, Tom (1985). Formulas for higher derivatives of the Riemann zeta function. Math. Comput. 44(169), 223–232.
[2] Guariglia, Emanuel (2021). Fractional calculus, zeta functions and Shannon entropy. Open Math. 19(1), 87–100.
[3] Guariglia, Emanuel (2019). Riemann zeta fractional derivative – functional equation and link with primes. Adv. Differ. Equ. 2019, Art. No. 261.
[4] Li, Chang-pin, Dao, Xuan Quy, Guo, Ping (2009). Fractional derivatives in complex planes. Nonlinear Anal. 71(5–6), 1857–1869.
[5] Ortigueira, Manuel Duarte, Coito, Fernando (2004). From differences to derivatives. Fract. Calc. Appl. Anal. 7(4), 459–471.
[6] Závada, Petr (1998). Operator of fractional derivative in the complex plane. Commun. Math. Phys. 192(2), 261–285.