Certain quantities transcendental over GF(pn,x)

Multizeta values for function fields: A survey

“…. [1] q n−1 , satisfying e(az) = C a (e(z)) (thus implying the formula for d n for n > 0, from its empty product case d 0 = 1 and recursion) and e(z) = 0 ↔ z ∈ Λ :=πA, for someπ ∈ C ∞ (known [52] to be transcendental over K) considered as analog of 2πi.…”

Subword complexity and finite characteristic numbers

“…Many of these finite characteristic numbers were shown to be transcendental over F q (T ) (see [18,14,20,21,22]). …”

Untitled

“…12 Since then, various approaches, tools and results,see eg Amou, 1 Brownawell, 2 Dammme and Hellegouarch, 4 Denis, 5 Geijsel, 7,8 Goss, 10 Mathan, 11 Wade, 12- 16 Yu, [17][18][19][20][21][22][23] have been investigated. Though the modern treatment of the subject via the concept of Drinfeld modules (Drinfeld 6 ) is dominating the present day research, the old and classical ideas and approach of Wade in 1941 still prove to be a direct and a very powerful technique of establishing certain specific transecndence results as evidenced in some recent works of Damamme and Hellegouarch.…”

“…Though the modern treatment of the subject via the concept of Drinfeld modules (Drinfeld 6 ) is dominating the present day research, the old and classical ideas and approach of Wade in 1941 still prove to be a direct and a very powerful technique of establishing certain specific transecndence results as evidenced in some recent works of Damamme and Hellegouarch. 4 A close analysis of the works of Wade [12][13][14][15][16] reveals that the ideas consist of first assuming algebraicity, second finding multipliers, third separating appropriate expressions into the so-called integral and remainder parts, fourth estimating upper and lower bounds for the integral and remainder parts and fifth and finally, deriving a contradiction from the upper and lower bounds or the like. The main objective of this work is to substantiate this belief by proving five theorems generalizing corresponding earlier results of Wade [12][13][14][15][16] basing on a careful analysis of the original method of Wade mentioned above.…”