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SUMMARY:Sreerupa Bhattacharjee (University of Lethbridge)
DTSTART:20231121T210000Z
DTEND:20231121T220000Z
DTSTAMP:20260423T021137Z
UID:NTC/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/34/">A S
 urvey of Büthe's Method for Estimating Prime Counting Functions</a>\nby S
 reerupa Bhattacharjee (University of Lethbridge) as part of Lethbridge num
 ber theory and combinatorics seminar\n\nLecture held in University of Leth
 bridge: M1060 (Markin Hall).\n\nAbstract\nThis talk will begin with a stud
 y on explicit bounds for $\\psi(x)$ starting with the work of Rosser in 19
 41. It will also cover various improvements over the years including the w
 orks of Rosser and Schoenfeld\, Dusart\, Faber-Kadiri\, Platt-Trudgian\, B
 üthe\, and Fiori-Kadiri-Swidinsky. In the second part of this talk\, I wi
 ll provide an overview of my master's thesis which is a survey on `Estimat
 ing $\\pi(x)$ and Related Functions under Partial RH Assumptions' by Jan B
 üthe. This article provides the best known bounds for $\\psi(x)$ for smal
 l values of~$x$ in the interval $[e^{50}\,e^{3000}]$. A distinctive featur
 e of this paper is the use of Logan's function and its Fourier Transform. 
 I will be presenting the main theorem in Büthe's paper regarding estimate
 s for $\\psi(x)$ with other necessary results required to understand the p
 roof.\n
LOCATION:https://researchseminars.org/talk/NTC/34/
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