show · character.dirichlet.values_on_gens all knowls · up · search:

A Dirichlet character $\chi\colon \Z\to \C$ of modulus $q$ is determined (via multiplicativity) by the values $\chi(g_1), \ldots, \chi(g_r)$ it takes on any list of generators $g_1,\ldots,g_r$ for the group $(\mathbb{Z}/q\mathbb{Z})^\times$. The generators $g_i$ can each be specified as integers in the interval $[1,q-1]$, and the values $\chi(g_i)$ are roots of unity $e(r):=\exp(2\pi i r)$, where $r$ is a rational number.

Authors:
Knowl status:
• Review status: reviewed
• Last edited by Pascal Molin on 2019-04-30 12:21:16
Referred to by:
History:
Differences
{"ft_lang_label":"__label__en","ft_lang_prob":0.62380135,"math_prob":0.9987007,"size":705,"snap":"2019-43-2019-47","text_gpt3_token_len":248,"char_repetition_ratio":0.105563484,"word_repetition_ratio":0.0,"special_character_ratio":0.38439715,"punctuation_ratio":0.1474359,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986819,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-20T03:04:00Z\",\"WARC-Record-ID\":\"<urn:uuid:aa3111fd-1c7b-4994-b3d5-ac008f6a36a4>\",\"Content-Length\":\"23156\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3d9e985b-9bf1-42cd-a7bd-2fb33b6e59da>\",\"WARC-Concurrent-To\":\"<urn:uuid:1e7927f0-73f6-4ac2-b23f-6967f6ab7378>\",\"WARC-IP-Address\":\"35.241.19.59\",\"WARC-Target-URI\":\"http://www.lmfdb.org/knowledge/show/character.dirichlet.values_on_gens\",\"WARC-Payload-Digest\":\"sha1:ACC32RGVQ5V2IEENVO2WLINH54E6LMVD\",\"WARC-Block-Digest\":\"sha1:KFBKBLZZOUSFXV7Z6UAGBJUCEFZFTUMH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986702077.71_warc_CC-MAIN-20191020024805-20191020052305-00402.warc.gz\"}"}