It is also known that the nontrivial zeros are symmetrically placed about the , a result which follows from the functional equation and the symmetry about the line . For if is a nontrivial zero, then is also a zero (by the functional equation), and then is another zero. But and are symmetrically placed about the line , since , and if , then . The Riemann hypothesis is equivalent to , where is the (Csordas 1994). It is also equivalent to the assertion that for some constant ,
2. Dinosaurs are a constant fascination for kids, and the "asteroid impact" has become the popularly accepted explanation for their demise. Very few people realize that this is still hotly contested. For an interesting variation on the theme of this lesson, consider using dinosaur extinction as your focus. For an excellent discussion of the different hypotheses on the likely cause of this extinction, get ed. by Judith Scotchmoor et al, published by the American Geological Institute (2002). Note especially chapter 12: Dinosaur Extinction: Changing Views (pages 99-106), where three hypotheses are presented and discussed. A very recent episode in this controversy was revealed in a news article (10 April, 2003) in which new core samples from the reputed crater suggest an alternative explanation. for a PDF copy of the brief article, along with a few review questions. For a more detailed presentation of this topic, go to our lesson.
Hypothesis sheet - Parenting Perfect
The Riemann hypothesis was computationally tested and found to be true for the first zeros by Brent (1982), covering zeros in the region ). S. Wedeniwski used ZetaGrid () to prove that the first trillion () nontrivial zeros lie on the . Gourdon (2004) then used a faster method by Odlyzko and Schönhage to verify that the first ten trillion () nontrivial zeros of the function lie on the . This computation verifies that the Riemann hypothesis is true at least for all less than 2.4 trillion. These results are summarized in the following table, where indicates a .
Younger Dryas impact hypothesis - Wikipedia
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