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UID:1dbac4ea8ee2815f497d22e5ed669f88
CATEGORIES:Experimental Mathematics Seminar
CREATED:20260326T204208
SUMMARY:Summing a challenging series
LOCATION:https://rutgers.zoom.us/j/95103383827    password: 6564120420
DESCRIPTION:<p style="color: #000000; font-family: 'Times New Roman'; font-size: medium
 ; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; 
 text-indent: 0px; text-transform: none; white-space: normal; widows: 2; wor
 d-spacing: 0px;">On the math-fun list, Neil Sloane posed the following prob
 lem: Let V(n) denote the integer formed by using the base 10 digits of n in
  base 11. It is classical that the series sum_n 1/V(n) converges. It is cha
 llenging to calculate a good approximation to its value. As a second, relat
 ed, problem find a good approximation to the subseries sum_p 1/V(p), where 
 the sum is over primes. It turned out that the first problem was efficientl
 y solved by two related methods described by Robert Baillie and Jean-Franco
 is Burnol. However, they do not appear to apply to the second sum, since th
 ey both depend, implicitly, on the fact that the language of digits in the 
 first problem is a regular language, and a recent result of Thomas Dubbe sh
 ows, in a technical sense, that the digits of primes are poorly approximate
 d by a regular language. In this talk I'll describe attempts at approximati
 ng the value of the second sum. They involve fractals, Fourier series, the 
 prime zeta function, and the Karamata inequality. The process of analyzing 
 this was helped, considerably, by experimentation, and seeing structure in 
 graphs of quantities related to the series.</p>
CONTACT: Victor Miller, Anduril Industries
DTSTAMP:20260826T213941
DTSTART;TZID=America/New_York:20260402T170000
DTEND;TZID=America/New_York:20260402T180000
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