On L-functions associated with the vector space of binary quadratic forms
نویسندگان
چکیده
منابع مشابه
Orbital L-functions for the Space of Binary Cubic Forms
We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from their intrinsic interest, the results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper.
متن کاملOn Binary Quadratic Forms with Semigroup Property
A quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all binary integer quadratic forms with semigroup property. If there is an integer bilinear map s such that f(s(x,y)) = f(x)f(y) for all vectors x and y from the integer 2-dimensional lattice, then the form f has semigr...
متن کاملOn Perfect Binary Quadratic Forms
A quadratic form f is said to be perfect if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all perfect binary integer quadratic forms. If there is an integer bilinear map s such that f(s(x, y)) = f(x)f(y) for all vectors x and y from the integer 2-dimensional lattice, then the form f is perfect. We give an explicit descri...
متن کاملZeta Functions for Equivalence Classes of Binary Quadratic Forms
They are sums of zeta functions for prehomogeneous vector spaces and generalizations of Epstein zeta functions. For the rational numbers and imaginary quadratic fields one can define these functions also for SL(2, ^-equivalence, which for convenience we call 1equivalence. The second function arises in the calculation of the Selberg trace formula for integral operators on L(PSL(2, (!?)\H) where ...
متن کاملOn Character Sums of Binary Quadratic Forms
We establish character sum bounds of the form ∣∣∣∣ ∑ a≤x≤a+H b≤y≤b+H χ(x + ky) ∣∣∣∣ < p−τH2, where χ is a nontrivial character (mod p), p 1 4 +ε < H < p, and |a|, |b| < p H. As an application, we obtain that given k ∈ Z\{0}, x + k is a quadratic non-residue (mod p) for some 1 ≤ x < p 1 2e. Introduction. Let k be a nonzero integer. Let p be a large prime and let H ≤ p. We are interested in the c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1993
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000004475