dirichlet ghanatva

ganit mein, primes key ack sett kaa dirichlet ghanatva (yaa vishleshanatmak ghanatva), jiska naam peater gustave lezoon dirichlet key naam parr rakhaa gayaa haye, sett key aakar kaa ack maap haye jiska upayog praakritik ghanatva kii tulanaa mein aasaan haye.
paribhasha.
yadi "a" abhaajya sankhyaon kaa ack upasamuchchay haye, tou "a" kaa dirichlet ghanatva"
seema haye
aggar maujood haye. dhyaan dein kii sootra _ 2 key roop mein sootra _ 3 (prime jeeta function dekhein), yeh bhee isake barabar haye
yeh abhivyakti aamtaur parr "poul" kaa crum hoti haye.
s" = 1 parr, (halanki samanya roop seey yeh vaastav mein ack dhruv naheen haye kyonki iska gair-samakalan crum haye), cumm seey cumm yadi yeh falan "s" kii (vaastavik) shakti kaa ack samroop falan haye, tou "s" = 1 key paas. udaaharan key liye, yadi "a" sabhi abhaajya kaa samooh haye, tou yeh reeman jeeta falan haye jisamen "s" = 1 parr crum 1 kaa ack dhruv haye, isaliye sabhi abhaajya key samooh mein dirichlet ghanatva 1 haye. 
adhik aam taur parr, koee bhee abhaajya rashiyon (yaa abhaajya shaktiyon) key anukram key dirichlet ghanatva koo paribhaashit curr sakata haye, sambhavatah punaraavrittiyon key saath, usee tarah seey.
guna.
yadi abhajyank "a" key upasamuchchay mein praakritik ghanatva haye, joe kii seema dwara diyaa gayaa haye
phir iska ack dirichlet ghanatva bhee haye, aur donon ghanatva samaan hain. 
haalaanki yeh aamtaur parr yeh dikhaana aasaan hotaa haye kii abhaajya rashiyon key ack samooh mein dirichlet ghanatva hotaa haye, aur yeh kaee uddeshyon key liye paryaapt haye. udaaharan key liye, ankganitiya pragati parr dirichlet kii pramey koo saabit karane mein, yeh dikhaana aasaan haye kii abhaajya rashiyon kaa dirichlet ghanatva
ack ankganitiya pragati mein "a" + "nb" ("a", "b" saha-raashi key liye) mein diriclet ghanatva 1/φ ("b") hotaa haye, joe yeh dikhaane key liye paryaapt haye kii aise abhaajya kii ack anant sankhya haye, lekin yeh dikhaana kathin haye kii yeh praakritik ghanatva haye. 
motey taur parr, yeh saabit karate hue kii abhaajya rashiyon key kuchh samooh mein gair-shoonya dirichlet ghanatva hotaa haye, aamtaur parr yeh darshana shamil hotaa haye kii kuchh "ell"-kaary "aiss" = 1 bindu parr gayab naheen hotey hain, jabaki yeh darshaate hue kii unakaa praakritik ghanatva yeh haye kii "ell"-karyon mein rekha parr koee shoonya naheen haye.
vyavhaar mein, yadi kuchh "praakritik roop seey honey vaale" abhaajya rashiyon key samooh mein dirichlet ghanatva hotaa haye, tou iska praakritik ghanatva bhee hotaa haye, lekin kritrim prati-udaaharan bhee mill sakata haih udaaharan key liye, abhaajya rashiyon kaa samooh jiska pahala dashamlav ank 1 haye, uska koee praakritik ghanatva naheen haye, lekin iska dirichlet ghanatva logg (2)/logg (10) haye.

