Geodesic
Rational summation of $p$-adic series
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 342-353 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Problem of the rational summation for a wide class of $p$-adic convergent series is considered. Here, rational summation means a method to obtain a rational sum of power series for a rational value of its variable. Formula suitable for this summation is derived. Conditions for rational summability are obtained. Rational summation is possible only for special forms of the series. It is shown that the inverse problem of rational summation is always solvable. This is illustrated by some characteristic examples. Possible rational (adelic) summation of divergent perturbative expansions in string theory, and quantum field theory, is discussed. 
@article{TMF_1994_100_3_a2,
     author = {B. G. Dragovich},
     title = {Rational summation of $p$-adic series},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {342--353},
     year = {1994},
     volume = {100},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a2/}
}
TY  - JOUR
AU  - B. G. Dragovich
TI  - Rational summation of $p$-adic series
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 342
EP  - 353
VL  - 100
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a2/
LA  - ru
ID  - TMF_1994_100_3_a2
ER  - 
%0 Journal Article
%A B. G. Dragovich
%T Rational summation of $p$-adic series
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 342-353
%V 100
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a2/
%G ru
%F TMF_1994_100_3_a2
B. G. Dragovich. Rational summation of $p$-adic series. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 342-353. http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a2/

[1] Volovich I. V., Class. Quantum Grav., 4 (1987), L83 ; Grossman B., Phys. Lett. B, 197 (1987), 101 ; Freund P. G. O., Olson M., Phys. Lett. B, 199 (1987), 186 ; Freund P. G. O., Witten E., Phys. Lett., 199 (1987), 191 ; Frampton P. H,, Okada Y., Ubriaco M. R., Phys. Lett., 213 (1988), 260 ; Aref'eva I. Ya., Dragović B. G., Volovich I. V., Phys. Lett., 209 (1988), 445 ; 212 (1988), 283 ; 214 (1988), 339 ; Chekhov L. O., Zinoviev Yu.M., Commun. Math. Phys., 130 (1990), 623 ; Freund P. G. O., J. Math. Phys., 33 (1992), 1148 | DOI | MR | DOI | MR | Zbl | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | Zbl | DOI | MR

[2] Alacoque C., Ruelle P., Thiran E., Verstegen D., Weyers J., Phys. Lett. B, 211 (1988), 59 ; Vladimirov V. S., Volovich I. V., Commun. Math. Phys., 123 (1989), 659 ; Spokoiny B. L., Phys. Lett. B, 221 (1989), 120 ; Meurice Y., Int. J. Mod. Phys. A, 4 (1989), 5133 ; Zelenov E. L., J. Math. Phys., 32 (1991), 147 ; Khrennikov A. Yu., J. Math. Phys., 32 (1991), 932 | DOI | MR | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[3] Roth B. D. B., Phys. Lett. B, 213 (1988), 263 ; Melzer E., Int. J. Mod. Phys. A, 4 (1989), 4877 ; Missarov M. D., Phys. Lett. B, 272 (1991), 36 ; Smirnov V. A., Commun. Math. Phys., 149 (1992), 623 | DOI | MR | DOI | MR | DOI | MR | DOI | MR | Zbl

[4] Dragović B. G., Frampton P. H., Urosevic B. V., Mod. Phys. Lett. A, 5 (1990), 1521 ; Dragović B. G., Mod. Phys. Lett., 6 (1991), 2301 ; Aref'eva I. Ya., Dragović B. G., Frampton P. H., Volovich I. V., Int. J. Mod. Phys. A, 6 (1991), 4341 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[5] Vladimirov V. S., Leningrad Math. J., 2 (1991), 1261 ; Zelenov E. L., J. Math. Phys., 33 (1992), 178 ; Khrennikov A. Yu., J. Math. Phys., 33 (1992), 1636, 1643 | MR | DOI | MR | Zbl | DOI | MR

[6] Schikhof W. H., Ultrametric Calculus, Cambridge U. P., Cambridge, 1984 | MR | Zbl

[7] Aref'eva I. Ya., Dragović B. G., Volovich I. V., Phys. Lett. B, 200 (1988), 512 | DOI | MR

[8] Dragović B. G., Phys. Lett. B, 256 (1991), 392 | DOI | MR

[9] Dragović B. G., Theor. Math. Phys., 93 (1992), 211 | DOI | MR | Zbl

[10] Dragović B. G., J. Math. Phys., 34:3 (1993) | DOI | MR | Zbl

[11] Gross D. J., Periwal V., Phys. Rev. Lett., 60 (1988), 2105 | DOI | MR