{"publisher":"World Scientific Publishing","oa":1,"publication_status":"published","volume":9,"month":"11","issue":"2","title":"Incomplete kloosterman sums and multiplicative inverses in short intervals","_id":"244","doi":" https://doi.org/10.1142/S1793042112501448","citation":{"short":"T.D. Browning, A. Haynes, International Journal of Number Theory 9 (2012) 481–486.","apa":"Browning, T. D., &#38; Haynes, A. (2012). Incomplete kloosterman sums and multiplicative inverses in short intervals. <i>International Journal of Number Theory</i>. World Scientific Publishing. <a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\">https://doi.org/ https://doi.org/10.1142/S1793042112501448</a>","ista":"Browning TD, Haynes A. 2012. Incomplete kloosterman sums and multiplicative inverses in short intervals. International Journal of Number Theory. 9(2), 481–486.","ama":"Browning TD, Haynes A. Incomplete kloosterman sums and multiplicative inverses in short intervals. <i>International Journal of Number Theory</i>. 2012;9(2):481-486. doi:<a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\"> https://doi.org/10.1142/S1793042112501448</a>","chicago":"Browning, Timothy D, and Alan Haynes. “Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals.” <i>International Journal of Number Theory</i>. World Scientific Publishing, 2012. <a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\">https://doi.org/ https://doi.org/10.1142/S1793042112501448</a>.","mla":"Browning, Timothy D., and Alan Haynes. “Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals.” <i>International Journal of Number Theory</i>, vol. 9, no. 2, World Scientific Publishing, 2012, pp. 481–86, doi:<a href=\"https://doi.org/ https://doi.org/10.1142/S1793042112501448\"> https://doi.org/10.1142/S1793042112501448</a>.","ieee":"T. D. Browning and A. Haynes, “Incomplete kloosterman sums and multiplicative inverses in short intervals,” <i>International Journal of Number Theory</i>, vol. 9, no. 2. World Scientific Publishing, pp. 481–486, 2012."},"type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"We investigate the solubility of the congruence xy ≡ 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums."}],"date_created":"2018-12-11T11:45:24Z","publication":"International Journal of Number Theory","intvolume":"         9","date_updated":"2021-01-12T06:57:30Z","quality_controlled":0,"date_published":"2012-11-30T00:00:00Z","year":"2012","day":"30","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning"},{"last_name":"Haynes","first_name":"Alan","full_name":"Haynes, Alan K"}],"publist_id":"7660","extern":1,"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council\tEPSRC,\nEP/J00149X/1\tEngineering and Physical Sciences Research Council\tEPSRC\t","page":"481 - 486","main_file_link":[{"url":"https://arxiv.org/abs/1204.6374","open_access":"1"}]}