Paperfolding, Automata, and Rational Functions - Diagonals and ...

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Algebraicity and Automaticity The phenomena we have just now noticed 1 automaticity 2 algebraicity in characteristic p 3 Mahler functional equation 4 regular p-substitutions are equivalent. It is a theorem of Giles Christol, Teturo Kamae, Michel Mendès France, and Gérard Rauzy that the Taylor coefficients of a power series defined over a finite field of characteristic p provide a p-automatic sequence if and only if the power series represents an algebraic function. Remarks of Loxton and mine add the identification with Mahler functions in characteristic zero. 22
Algebraicity and Automaticity The phenomena we have just now noticed 1 automaticity 2 algebraicity in characteristic p 3 Mahler functional equation 4 regular p-substitutions are equivalent. It is a theorem of Giles Christol, Teturo Kamae, Michel Mendès France, and Gérard Rauzy that the Taylor coefficients of a power series defined over a finite field of characteristic p provide a p-automatic sequence if and only if the power series represents an algebraic function. Remarks of Loxton and mine add the identification with Mahler functions in characteristic zero. 22
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Paperfolding, Automata, and Rationa
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Paperfolding, Automata, and Rationa
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Paperfolding Take a rectangular she
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A Mahler Functional Equation Aside.
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Next, if we pair the sequence Regul
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Next, if we pair the sequence Regul
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The uniform, or regular, 2-substitu
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Characteristic Functions I found th
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An Algebraic Equation in Characteri
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These remarks show that the paperfo
Page 77 and 78: These remarks show that the paperfo
Page 79 and 80: The Thue-Morse Sequence 0 1 10 11 1
Page 81 and 82: The Thue-Morse Sequence 0 1 10 11 1
Page 83 and 84: Euler’s Identity and a Functional
Page 89 and 90: An Algebraic Equation The function
Page 91 and 92: A Counter-example in Analysis I cla
Page 97 and 98: The Shapiro Sequence Consider, the
Page 107 and 108: A Remark on the Shapiro Function Se
Page 113: A Remark on the Shapiro Function Se
Page 116 and 117: Transcendence of Automatic Numbers
Page 122 and 123: Complexity of a Sequence Given an i
Page 124: Complexity of a Sequence Given an i
Page 127: Algebraicity and Automaticity The p
Page 131 and 132: Algebraicity and Automaticity The p
Page 133 and 134: Algebraicity and Automaticity The p
Page 135 and 136: Comments on the Proof The best proo
Page 141 and 142: But for expansions over the complex
Page 143 and 144: But for expansions over the complex
Page 145: But for expansions over the complex
Page 148 and 149: Power Series in Several Variables R
Page 158 and 159: Diagonals and Hadamard Products The
Page 160 and 161: Diagonals and Hadamard Products The
Page 162 and 163: A Theorem of Furstenberg It follows
Page 168 and 169: As said, in characteristic zero, ne
Page 174 and 175: A Beautiful Transcendence Argument
Page 176 and 177: A Beautiful Transcendence Argument
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Breaking Up in Characteristic p The
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Algebraic power series in character
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Hence, since Fp is finite, there ar
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Hence, since Fp is finite, there ar
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Suppose the series P aνx ν is gen
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So we have: Theorem. P aνx ν ∈
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The Lifting Theorem Looking careful
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Diagonals of Rational Functions Now
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Whilst (i) and (ii) are reasonably
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References MICHEL DEKKING, MICHEL M
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