{"product_id":"9780857099426","title":"Complex Numbers: Lattice Simulation and Zeta Function Applications","description":"An informative and useful account of complex numbers that includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the ever-elusory Riemann hypothesis. Stephen Roy assumes no detailed mathematical knowledge on the part of the reader and provides a fascinating description of the use of this fundamental idea within the two subject areas of lattice simulation and number theory.  Complex Numbers offers a fresh and critical approach to research-based implementation of the mathematical concept of imaginary numbers. Detailed coverage includes:\u003cul\u003e\n\u003cli\u003eRiemann’s zeta function: an investigation of the non-trivial roots by Euler-Maclaurin summation.\u003c\/li\u003e\n\u003cli\u003eBasic theory: logarithms, indices, arithmetic and integration procedures are described.\u003c\/li\u003e\n\u003cli\u003eLattice simulation: the role of complex numbers in Paul Ewald’s important work of the I 920s is analysed.\u003c\/li\u003e\n\u003cli\u003eMangoldt’s study of the xi function: close attention is given to the derivation of N(T) formulae by contour integration.\u003c\/li\u003e\n\u003cli\u003eAnalytical calculations: used extensively to illustrate important theoretical aspects.\u003c\/li\u003e\n\u003cli\u003eGlossary: over 80 terms included in the text are defined.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cul\u003e\n\u003cli\u003eOffers a fresh and critical approach to the research-based implication of complex numbers\u003c\/li\u003e\n\u003cli\u003eIncludes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the Riemann hypothesis\u003c\/li\u003e\n\u003cli\u003eBridges any gaps that might exist between the two worlds of lattice sums and number theory\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":47113512419568,"sku":"9780857099426","price":62.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780857099426_p0.jpg?v=1763827591","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780857099426","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}