On p -adic L -functions and the Riemann-Hurwitz genus formula

Warren M. Sinnott

Compositio Mathematica (1984)

  • Volume: 53, Issue: 1, page 3-17
  • ISSN: 0010-437X

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Sinnott, Warren M.. "On $p$-adic $L$-functions and the Riemann-Hurwitz genus formula." Compositio Mathematica 53.1 (1984): 3-17. <http://eudml.org/doc/89676>.

@article{Sinnott1984,
author = {Sinnott, Warren M.},
journal = {Compositio Mathematica},
keywords = {Iwasawa class number formula; Riemann-Hurwitz genus formula; value of - functions at ; CM-field; cyclotomic tower; -adic -functions; totally real fields; -adic pseudomeasures; relation between analytic -invariants; Kida's formula; analytic class number formula},
language = {eng},
number = {1},
pages = {3-17},
publisher = {Martinus Nijhoff Publishers},
title = {On $p$-adic $L$-functions and the Riemann-Hurwitz genus formula},
url = {http://eudml.org/doc/89676},
volume = {53},
year = {1984},
}

TY - JOUR
AU - Sinnott, Warren M.
TI - On $p$-adic $L$-functions and the Riemann-Hurwitz genus formula
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 53
IS - 1
SP - 3
EP - 17
LA - eng
KW - Iwasawa class number formula; Riemann-Hurwitz genus formula; value of - functions at ; CM-field; cyclotomic tower; -adic -functions; totally real fields; -adic pseudomeasures; relation between analytic -invariants; Kida's formula; analytic class number formula
UR - http://eudml.org/doc/89676
ER -

References

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  1. [1] P. Cassou-Noguès: Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques. Inv. Math.51 (1979) 29-59. Zbl0408.12015MR524276
  2. [2] J. Coates: p-adic L-functions and Iwasawa theory. In: Algebraic Number Fields, ed. by A. Fröhlich, Academic Press, New York (1977) pp. 269-353. Zbl0393.12027MR460282
  3. [3] C. Chevalley and A. Weil: Über das Verhalten der Integrale erster Gattung bei Automorphismen des Funktionenkörpers. Hamb. Abh.10 (1934) 358-361. Zbl0009.16001JFM60.0098.01
  4. [4] P. Deligne and K. Ribet: Values of abelian L-functions at negative integers over totally real fields. Inv. Math.59 (1980) 227-286. Zbl0434.12009MR579702
  5. [5] Leslie Jane Federer: Ph.D. thesis, Princeton Univ., Princeton, 1982. 
  6. [6] G. Gras, Sur la construction des fonctions L p-adiques abéliennes, Seminaire Delange-Pisot-Poitou (Théorie des nombres), 1978/79, n° 22. Zbl0427.12014MR582430
  7. [7] G. Gras, Sur les invariants lambda d'Iwasawa des corps abéliens. Pub. Math. de la Fac. des Sci. de Besançon (1978/79). Zbl0472.12009
  8. [8] K. Iwasawa: On r-extensions of algebraic number fields. Bull. Amer. Math. Soc.65 (1959) 183-226. Zbl0089.02402MR124316
  9. [9] K. Iwasawa: Lectures on p-adic L-functions. Ann. Math. Studies74, Princeton University Press, Princeton (1972). Zbl0236.12001MR360526
  10. [10] K. Iwasawa: Riemann-Hurwitz formula and p-adic Galois representations for number fields. Tôhoku Math. J. (Second Series) 33(2) (1981) 263-288. Zbl0468.12004MR624610
  11. [11] Y. Kida: l-extensions of CM-fields and cyclotomic invariants. J. Number Theory12 (1980) 519-528. Zbl0455.12007MR599821
  12. [12] K. Ribet: Report on p-adic L-functions over totally real fields. Soc. Math. de France, Astérisque61 (1979) 177-192. Zbl0408.12016MR556672
  13. [13] J.-P. Serre: Sur le résidu de la fonction zêta p-adique d'un corps de nombres. C.R. Acad. Sc. Paris287 (1978) 183-188. Zbl0393.12026MR506177

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