According to A Comprehensive Grammar of the English Language, the relationship that underlies this construction is not that of "noun + adverbial" since there is found in the combination an identity of reference for the two nouns. This is characteristic of apposition.
(CoGEL § 17.65) The nature of apposition
[…] Apposition is primarily, and typically, a relation hetween noun phrases […]. For linguistic units to be APPOSITIVES, ie in apposition, they must normally be identical in reference. Thus in [1], Anna and my best friend are coreferential […]
- Anna, my best friend,was here last night. [1]
Alternatively, the reference of one must be included in the reference of the other, eg [3], where a neighbour is identified as Fred Brick:
- A neighbour, Fred Brick, is on the telephone.
The relationship denoted by apposition is therefore analogous to a copular relationship.
- Fred Brick is a neighbour.
This is verifiable for "the letter L" and "the number 3".
- L is a letter, 3 is a number
(CoGEL § 17.66) Full and partial apposition
Grammarians vary in the freedom with which they apply the term 'apposition' even in the quite specific sense adopted here. Some have restricted it more narrowly to cases where the following conditions are met:
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(i) Each of the appositives can be separetely omitted without affecting the acceptability of the sentence.
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(ii) Each fulfils the same syntactic function in the resultant sentences.
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(iii) It can be assumed that there is no difference between the original
sentence and either of the resultant sentences in extralinguistic reference.
For example, by omitting each appositive in turn from [1] we obtain the two
sentences [1a] and [1bl:
- A neighbour, Fred Brick, is on the telephone. [1]
- A neighbour is on the telephone. [1a]
- Fred Brick is on the telephone. [1b]
The apposition in [1] meets the three conditions:
(i) The resultant sentences are acceptable.
(ii) Both noun phrases are subject of their sentence.
(iii) Since Fred Brick and a neighbour are coreferential in [1], we can
assume the reference of the two resultant sentences to be the same.
Apposition meeting these three conditions we term FULL APPOSITION.
This is true of the sentences that follow.
- The letter L comes after K. - The number 3 is divisible by 3.
- L comes after K. - The letter comes after K.
It can be concluded that those constructions are cases of full apposition, and further properties of apposition that they show seem to confirm this contention.
(CoGEL § 17.67) Strict and weak apposition
The appositives may belong to the same general syntactic class (eg the central type noun phrase + noun phrase), as in [1]:
- Football, his only interest in life, has brought him many friends. [1]
In such a case we term the construction STRICT APPOSITION.
[…]
This is true for these constructions: L, "letter", 3 and "number" are nouns.
(CoGEL § 17.69) Defined\defining relationships
When apposition is full apposition […], it may not be clear which of the appositives is the defining one:
- My friend Anna was here last night. [full + strict]
As concerns the OP's construction it is clear that "letter" defines what L is and that "number" defines what 3 is.
(CoGEL § 17.68) Nonrestrictive and restrictive apposition
Apposition may be NONRESTRICTIVE or RESTRICTIVE […]. The appositives in nonrestrictive apposition are in separate information units […]. This fact is
indicated, in speech, by their inclusion in separate tone units […]; in writing, by their separation by commas or heavier punctuation. For
example, the apposition is nonrestrictive in [1] hut restrictive in [1a]:
- Mr Campbell, a lawyer, was here last night. [1]
- Mr Campbell the lawyer, was here last night. [ie Mr Campbell the lawyer as opposed to any other Mr Campbell we know] [1a]
This applies to the OP's constructions: "the letter L as opposed to any other letter".
The following example in CoGEL, § 17.70, which is labelled "FULL, STRICT, RESTRICTIVE" shows a similar pattern.
- My friend Anna was here last night. (My friend Anna as opposed to any other friend)