O transformaci řad v řady rychleji konvergentní se zvláštním zřetelem k zobecněné harmonické řadě . [III.]
O transformaci řad v řady rychleji konvergentní se zvláštním zřetelem k zobecněné harmonické řadě . II.
O transformaci řad v řady rychleji konvergentní se zvláštním zřetelem k zobecněné harmonické řadě . [I.]
On a functional equation satisfied by certain Dirichlet series
On a two-variable -adic -function.
On a two-variable zeta function for number fields
This paper studies a two-variable zeta function attached to an algebraic number field , introduced by van der Geer and Schoof, which is based on an analogue of the Riemann-Roch theorem for number fields using Arakelov divisors. When this function becomes the completed Dedekind zeta function of the field . The function is a meromorphic function of two complex variables with polar divisor , and it satisfies the functional equation . We consider the special case , where for this function...
On Cantor's singular moments.
On characterization of Dirichlet L-functions
On Cramér's theorem for general Euler products with functional equation.
On Epstein's Zeta-function.
On evaluations of infinite double sums and Tornheim's double series.
On general L-functions
On Hecke -functions associated with cusp forms. II: On the sign changes of .
On Hecke L-functions associated with cusp forms
On limit distribution of the Matsumoto zeta-function
On Li’s Coefficients for Some Classes of L-Functions
AMS Subj. Classification: 11M41, 11M26, 11S40We study the generalized Li coefficients associated with the class S♯♭ of functions containing the Selberg class and (unconditionally) the class of all automorphic L-functions attached to irreducible unitary cuspidal representations of GLN(Q) and the class of L-functions attached to the Rankin-Selberg convolution of two unitary cuspidal automorphic representations π and π′ of GLm(AF ) and GLm′ (AF ). We deduce a full asymptotic expansion of the Archimedean...
On Mellin-barnes Type of Integrals and Sumsassociated With the Riemann Zeta-function}
On multiple analogues of Ramanujan’s formulas for certain Dirichlet series
In this paper, we prove multiple analogues of famous Ramanujan’s formulas for certain Dirichlet series which were introduced in his well-known notebooks. Furthermore, we prove some multiple versions of analogous formulas of Ramanujan which were given by Berndt and so on.
On Popov's explicit formula and the Davenport expansion
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function with the periodic Bernoulli polynomial weight and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order or gives the well-known explicit formula for respectively the partial...
On q-orders in primitive modular groups
We prove an upper bound for the number of primes p ≤ x in an arithmetic progression 1 (mod Q) that are exceptional in the sense that has no generator in the interval [1,B]. As a consequence we prove that if with a sufficiently large absolute constant c, then there exists a prime q dividing Q such that for some positive integer b ≤ B. Moreover we estimate the number of such q’s under suitable conditions.