
CBMS Regional Conference Series in Mathematics 1977; 41 pp; softcover Number: 32 ISBN10: 0821838806 ISBN13: 9780821838808 List Price: US$24 Member Price: US$19.20 All Individuals: US$19.20 Order Code: CBMS/32.D Suggest to a Colleague Please note that AMS On Demand titles are not returnable.  Knowledge about fractional parts of linear polynomials is fairly satisfactory. Knowledge about fractional parts of nonlinear polynomials is not so satisfactory. In these notes the author starts out with Heilbronn's Theorem on quadratic polynomials and branches out in three directions. In Sections 712 he deals with arbitrary polynomials with constant term zero. In Sections 1319 he takes up simultaneous approximation of quadratic polynomials. In Sections 2021 he discusses special quadratic polynomials in several variables. There are many open questions: in fact, most of the results obtained in these notes ar almost certainly not best possible. Since the theory is not in its final form including the most general situation, i.e. simultaneous fractional parts of polynomials in several variables of arbitary degree. On the other hand, he has given all proofs in full detail and at a leisurely pace. For the first half of this work, only the standard notions of an undergraduate number theory course are required. For the second half, some knowledge of the geometry of numbers is helpful. 


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