Let X be a projective, irreducible, nonsingular algebraic curve over the finite field F q with q elements and let |X (F q )| and g(X ) be its number of rational points and genus respectively. The Ihara constant A(q) has been intensively studied during the last decades, and it is defined as the limit superior of |X (F q )|/g(X ) as the genus of X goes to infinity. In [9] an analogue D(q) of A(q) is defined, where the nonsingularity of X is dropped and g(X ) is replaced with the degree of X . We will call D(q) Homma's constant. In this paper, upper and lower bounds for the value of D(q) are found.
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