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DTSTART;TZID=Asia/Kolkata:20210310T150000
DTEND;TZID=Asia/Kolkata:20210310T160000
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SUMMARY:Dr Gaurav Bhatnagar to interact on "The Partition-Frequency Enumeration Matrix"
DESCRIPTION:Progressing with the series of Departmental Seminars\, Department of Mathematics\, SRM University-AP\, Andhra Pradesh invites Dr Gaurav Bhatnagar\, Visiting Associate Professor\, Department of Mathematics\, Ashoka University to deliver a lecture titled “The Partition-Frequency Enumeration Matrix” on March 10\, 2021\, at 3 PM. \nThe Partition-Frequency Enumeration (PFE) matrix is an infinite upper-triangular number-theoretic matrix that is used to enumerate partition-like objects as an elementary approach. This matrix unifies voluminous results connecting number-theoretic functions to partition-type functions. The calculus is extended to arbitrary generating functions and functions with Weierstrass products. As a by-product\, some well-known recurrence relations for many number-theoretic functions are recovered. These include the sum of divisors function\, Ramanujan’s $tau$ function\, sums of squares and triangular numbers\, and $zeta(2n)$\, where $n$ is a positive integer. As an application\, Ramanujan’s famous congruences $p(5n+4)equiv 0$ (mod $5)$ and $tau(5n+5)equiv 0$ (mod $5)$ are embedded into an infinite family of such congruences. During the lecture\, Dr Gaurav Bhatnagar will highlight two other congruence results concerning the sum of the divisor function.
URL:https://events.srmap.edu.in/event/dr-gaurav-bhatnagar-to-interact-on-the-partition-frequency-enumeration-matrix/
CATEGORIES:Events,Math Events,Webinars
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