zbMATH — the first resource for mathematics

Rational summation of \(p\)-adic series. (English) Zbl 0860.11070
Theor. Math. Phys. 100, No. 3, 1055-1064 (1994) and Teor. Mat. Fiz. 100, No. 3, 342-353 (1994).
Certain \(p\)-adic power series, their domain of convergence, and the problem as to whether the sum is rational for some rational value of the variable, are discussed. Examples of such series are given. In the introduction the connection with \(p\)-adic quantum field theory is explained.
Note of the reviewer: In section 5 of the paper it is stated that \(\sum n!\) cannot be rational in every \(\mathbb{Q}_p\) \((p\) prime). However, according to the quoted reference, it is only known that the sum cannot be rational in every \(\mathbb{Q}_n\) \((n \in \mathbb{N},\;n \geq 2)\).

11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
30B10 Power series (including lacunary series) in one complex variable
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
Full Text: DOI
[1] I. V. Volovich,Class. Quantum Grav.,4, L83 (1987); B. Grossman,Phys. Lett.,B197, 101 (1987); P. G. O. Freund and M. Olson,Phys. Lett.,B199, 186 (1987); P. G. O. Freund and E. Witten,Phys. Lett.,199, 191 (1987); P. H. Frampton, Y. Okada, and M. R. Ubriaco,Phys. Lett.,213, 260 (1988); I. Ya. Aref’eva, B. G. Dragović, and I. V. Volovich,Phys. Lett.,209, 445 (1988);212, 283 (1988);214, 339 (1988); L. O. Chekhov and Yu. M. Zinoviev,Commun. Math. Phys.,130, 623 (1990); P. G. O. Freund,J. Math. Phys.,33, 1148 (1992). · doi:10.1088/0264-9381/4/4/003
[2] C. Alacoque, P. Ruelle, E. Thiran, D. Verstegen, and J. Weyers,Phys. Lett.,B211, 59 (1988); V. S. Vladimirov and I. V. Volovich,Commun. Math. Phys.,123, 659 (1989); B. L. Spokoiny,Phys. Lett.,B221, 120 (1989); Y. Meurice,Int. J. Mod. Phys.,A4, 5133 (1989); E. I. Zelenov,J. Math. Phys.,32, 147 (1991); A. Yu. Khrennikov,J. Math. Phys.,32, 932 (1991).
[3] B. D. B. Roth,Phys. Lett.,B213, 263 (1988); E. Melzer,Int. J. Mod. Phys.,A4, 4877 (1989); M. D. Missarov,Phys. Lett.,B272, 36 (1991); V. A. Smirnov,Commun. Math. Phys.,149, 623 (1992). · doi:10.1016/0370-2693(88)91758-3
[4] B. G. Dragović, P. H. Frampton, and B. V. Urošević,Mod. Phys. Lett.,A5, 1521 (1990); B. G. Dragović,Mod. Phys. Lett.,6, 2301 (1991); I. Ya. Aref’eva, B. G. Dragović, P. H. Frampton, and I. V. Volovich,Int. J. Mod. Phys.,A6, 4341 (1991). · Zbl 1020.83500 · doi:10.1142/S0217732390001748
[5] V. S. Vladimirov,Leningrad Math. J.,2, 1261 (1991); E. I. Zelenov,J. Math. Phys.,33, 178 (1992); A. Yu. Khrennikov,J. Math. Phys.,33, 1636, 1643 (1992).
[6] W. H. Schikhof,Ultrametric Calculus, Cambridge Univ. Press, Cambridge (1984). · Zbl 0553.26006
[7] I. Ya. Aref’eva, B. G. Dragović, and I. V. Volovich,Phys. Lett.,B200, 512 (1988). · doi:10.1016/0370-2693(88)90161-X
[8] B. G. Dragović,Phys. Lett.,B256, 392 (1991). · doi:10.1016/0370-2693(91)91780-Y
[9] B. G. Dragović,Theor. Math. Phys.,93, 211 (1992).
[10] B. G. Dragović,J. Math. Phys.,34, No. 3 (1993).
[11] D. J. Gross and V. Periwal,Phys. Rev. Lett.,60, 2105 (1988). · doi:10.1103/PhysRevLett.60.2105
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.