LEADER 03566oam 2200805I 450 001 9910962078403321 005 20240516095738.0 010 $a9786613908650 010 $a9781040188101 010 $a1040188109 010 $a9780429067617 010 $a0429067615 010 $a9781283596206 010 $a1283596202 010 $a9781466501935 010 $a1466501936 024 7 $a10.1201/b11315 035 $a(CKB)2550000000079197 035 $a(EBL)830246 035 $a(OCoLC)773034262 035 $a(SSID)ssj0000581416 035 $a(PQKBManifestationID)11370656 035 $a(PQKBTitleCode)TC0000581416 035 $a(PQKBWorkID)10531248 035 $a(PQKB)10632004 035 $a(Au-PeEL)EBL830246 035 $a(CaPaEBR)ebr10522560 035 $a(CaONFJC)MIL390865 035 $a(OCoLC)1287180530 035 $a(FINmELB)ELB158667 035 $a(MiAaPQ)EBC830246 035 $a(EXLCZ)992550000000079197 100 $a20180331d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on N_X (p) /$fJean-Pierre Serre 205 $a1st ed. 210 $aBoca Raton, Fla. $cCRC Press$dc2012 210 1$aBoca Raton, Fla. :$cCRC Press,$d2012. 215 $a1 online resource (168 p.) 225 1 $aResearch notes in mathematics ;$vv. 11 300 $aAn AK Peters book. 311 08$a9781466501928 311 08$a1466501928 320 $aIncludes bibliographical references. 327 $aFront Cover; Contents; Preface; Conventions; Chapter 1. Introduction; Chapter 2. Examples; Chapter 3. The Chebotarev Density Theorem for a Number Field; Chapter 4. Review of l-adic Cohomology; Chapter 5. Auxiliary Results on Group Representations; Chapter 6. The l-adic Properties of NX(p); Chapter 7. The Archimedean Properties of NX(p); Chapter 8. The Sato-Tate Conjecture; Chapter 9. Higher Dimension: the Prime Number Theorem and the Chebotarev Density Theorem; References 330 $aThis book presents several basic techniques in algebraic geometry, group representations, number theory, -adic and standard cohomology, and modular forms. It explores how NX(p) varies with p when the family (X) of polynomial equations is fixed. The text examines the size and congruence properties of NX(p) and describes the ways in which it is computed. Along with covering open problems and offering simple, illustrative examples, the author presents various theorems, including the Chebotarev density theorem and the prime number theorem--$cProvided by publisher. 330 $aThe main topic involves counting solutions mod p of a system of polynomial equations, as p varies. The book is based on a series of lectures presented by the author in Taiwan. Using this idea, Serre visits algebra and number theory and asks some non-standard questions, especially on group representations--$cProvided by publisher. 410 0$aResearch notes in mathematics ;$v11. 606 $aPolynomials 606 $aNumber theory 606 $aRepresentations of groups 606 $aCohomology operations 615 0$aPolynomials. 615 0$aNumber theory. 615 0$aRepresentations of groups. 615 0$aCohomology operations. 676 $a512.9/422 686 $aMAT022000$2bisacsh 700 $aSerre$b Jean-Pierre$f1926,$01790835 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962078403321 996 $aLectures on N_X (p)$94327585 997 $aUNINA