Equazioni differenziali p -adiche e interpolazione p -adica di formule classiche

Francesco Baldassarri

Bollettino dell'Unione Matematica Italiana (2000)

  • Volume: 3-B, Issue: 3, page 573-600
  • ISSN: 0392-4041


We shortly introduce non-archimedean valued fields and discuss the difficulties in the corresponding theory of analytic functions. We motivate the need of p -adic cohomology with the Weil Conjectures. We review the two most popular approaches to p -adic analytic varieties, namely rigid and Berkovich analytic geometries. We discuss the action of Frobenius in rigid cohomology as similar to the classical action of covering transformations. When rigid cohomology is parametrized by twisting characters, Frobenius is a source of interesting p -adic analytic functions of those characters, like Morita's p -adic gamma function Γ p . We conclude with some more examples of this phenomenon in connection with Gauss generalized hypergeometric equation and with an integral formula of Selberg.

How to cite


Baldassarri, Francesco. "Equazioni differenziali $p$-adiche e interpolazione $p$-adica di formule classiche." Bollettino dell'Unione Matematica Italiana 3-B.3 (2000): 573-600. <http://eudml.org/doc/194982>.

author = {Baldassarri, Francesco},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {-adic interpolation; -adic differential equations; Gross-Koblitz formula; Morita’s -adic gamma function; Koblitz-Diamond formula; hypergeoemtric functions},
language = {ita},
month = {10},
number = {3},
pages = {573-600},
publisher = {Unione Matematica Italiana},
title = {Equazioni differenziali $p$-adiche e interpolazione $p$-adica di formule classiche},
url = {http://eudml.org/doc/194982},
volume = {3-B},
year = {2000},

AU - Baldassarri, Francesco
TI - Equazioni differenziali $p$-adiche e interpolazione $p$-adica di formule classiche
JO - Bollettino dell'Unione Matematica Italiana
DA - 2000/10//
PB - Unione Matematica Italiana
VL - 3-B
IS - 3
SP - 573
EP - 600
LA - ita
KW - -adic interpolation; -adic differential equations; Gross-Koblitz formula; Morita’s -adic gamma function; Koblitz-Diamond formula; hypergeoemtric functions
UR - http://eudml.org/doc/194982
ER -


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